Summer School and Workshop on Lie Theory andRepresentation Theory (SSW-LTRT) IV

• Time of Summer SchoolJune 28-July 9, 2015 (the first period) andJuly 13-July 22, 2015 (the second period)

• Time of WorkshopJuly 2-July 4, 2015

• Sitehttp://math.ecnu.edu.cn/academia/lie2015

• SponsorEast China Normal University

• Organizing BoardOrganizers: Scientific Committee:Bin Shu (ÓR) Naihong Hu (�Dù¤Weiqiang Wang (��r) Hebing Rui (�ÚW¤

Jianyi Shi (�|Ã)Jianpan Wang (�ï�)

Technology Support: Contact:Hao Chang (~Ó) Husileng Xiao (��de)Husileng Xiao (��de)

• Venues of Workshop and Summer SchoolWorkshop: Room 102, Teaching building No. 3 (1n�Æ¢102�¿)Summer School: Teaching Buildings No.1, No.2 and No.4

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“ECNU Summer School and workshop on Lie theory and representation theoryIV, June 28-July 9, July 13-July 22, 2015” will be held at the new campus of EastChina Normal University in Min Hang District of Shanghai. This summer schooland workshop is a sequel to the ones held in 2006, 2009 and 2012 respectively (seehttp://math.ecnu.edu.cn/academia/lie2015/2012/index.htm for the formers).

The theme of the two periods of summer school is representation theory withconnection to geometry. In addition, there will be a workshop on the 2nd, the 3rdand the 4th of July.

Lecturers of Summer School

Pramod N. Achar (Louisiana State University)

Ivan Losev (Northeastern University)

Peng Shan (CNRS researcher, University of Paris-Sud)

Weiqiang Wang (University of Virginia)

Invited Speakers of WorkshopPramod N. Achar (Louisiana State University)

Tomoyuki Arakawa (Kyoto University)

Shun-Jen Cheng (Academia Sinica, Taipei)

Weideng Cui (Tsinghua Univesity)

Chongying Dong (UC Santa Cruz)

Jie Du (University of New South Walse)

Zhaobing Fan (Harbin Engineering University)

Rolf Farnsteiner (Christian-Albrichits Universitat Zu Kiel)

Cuipo Jiang (Shanghai Jiaotong University)

Jae-Hoon Kwon (Sungkyunkwan University)

Ivan Losev (Northeastern University)

Satoshi Naito (Tokyo Institute of Technology)

Peng Shan (CNRS researcher, University of Paris-Sud)

Toshiaki Shoji (Tongji University)

Jinkui Wan (Beijing Institute of Technology)

Weiqiang Wang (University of Virginia)

Nanhua Xi (Chinese Academy of Science)

Yang Zeng (Nanjing Audit University)

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1 WORKSHOP

1 Workshop

1.1 Schedule of Talks in the Workshop

(Venue: Room 102 Teaching building 3 (1n�Ƣ102))

July 2-4 July 2 July 3 July 4

(Thursday) (Friday) (Saturday)

8:00 - 8:20 Registration

8:20 - 8:30 Welcome Speech

8:30 - 9:25 Shoji Chongying Dong Nanhua Xi

9:40 - 10:35 Arakawa Jie Du Farnsteiner

10:35 - 11:00 Tea Break Tea Break Tea Break

11:00 - 11:55 Peng Shan Cuipo Jiang Naito

Group Photo

14:00 - 14:55 Losev Shun-Jen Cheng Achar

15:10 - 16:05 Jinkui Wan Weiqiang Wang Zhaobing Fan

16:05 - 16:30 Tea Break Tea Break Tea Break

16:30 - 17:25 Yang Zeng Kwon Weideng Cui

1.2 Program of Workshop

July 2 (Thu)

8:20- 8:30 Welcome Speeches8:30- 9:25 T. Shoji (Tongji University)

Springer correspondence for complex reflection groupsand related Kostka functions

9:40- 10:35 Tomoyuki Arakawa (Kyoto University)Joseph ideals and lisse minimal W-algebras

10:35- 11:00 Tea Break

11:00- 11:55 Peng Shan (CNRS researcher, University of Paris-Sud)On the center of quiver Hecke algebras

12:00- Group Photo

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1.2 Program of Workshop 1 WORKSHOP

Lunch Time

14:00- 14:55 Ivan Losev (Northeastern University)Quantizations of nilpotent orbits

15:10- 16:05 Jinkui Wan (Beijing Institute of Technology)Frobenius map for the centers of Hecke algebras

16:05- 16:30 Tea Break

16:30- 17:25 Yang Zeng (Nanjing Audit University)Finte W-superalgebras for basic Lie superalgebras and their applications

July 3 (Fri)

8:30- 9:25 Chongying Dong (UC Sant Cruz)On orbifold theory

9:40- 10:35 Jie Du ( University of New South Wales)Quantum linear supergroups and their canonical bases

10:35- 11:00 Tea Break

11:00- 11:55 Cuipo Jiang (Shanghai Jiaotong University)Coset vertex operator algebras from tensor decomposition of affine vertex operator algebras

Lunch Time

14:00- 14:55 Shun-Jen Cheng (Academia Sinica)Finite-dimensional representations of the queer Lie superalgebra of half-integer weights

15:10- 16:05 Weiqiang Wang (University of Virginia)Canonical bases for tensor product modules

16:05- 16:30 Tea Break

16:30- 17:25 Jae-Hoon Kwon (Sungkyunkwan University)Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras

July 4 (Sat)

8:30- 9:25 Nanhua Xi (Chinese Academy of Science)Representations in rational functions

9:40- 10:35 R. Farnsteiner (Christian-Albrichits Univeristitat Zu Kiel)Degrees of modules and varities of elementary abelian Lie algebras

11:00- 11:55 Satoshi Naito (Tokyo Institute of Technology)Specializations of symmetric Macdonald polynomials and pseudoQLS paths

Lunch Time

14:00- 14:55 Pramod N. Achar (Louisiana State University)Modular perverse sheaves on the affine Grassmannian

15:10- 16:05 Zhaobing Fan (Harbin Engineering University)Equivalence of representation categories of various quantum and super quantum groups

16:05- 16:30 Tea Break

16:30- 17:25 Weideng Cui (Tsinghua University)Affine cellularity of some infinite-dimensional algebras

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1.3 Abstracts of Workshop Talks 1 WORKSHOP

1.3 Abstracts of Workshop Talks

♣ Pramod N. Achar (Louisiana State University)Modular perverse sheaves on the affine Grassmannian (July 4, 14:00-14:55)

Perverse sheaves on the affine Grassmannian of a reductive group G encode a great deal ofrepresentation-theoretic information. In characteristic 0, these sheaves have been studied in depthsince the 1990s. In this talk, I will discuss recent advances in the positive-characteristic case, includ-ing the proof of the Mirkovic-Vilonen conjecture and the relationship with the Springer resolutionof the Langlands dual group. This is joint work with L. Rider. I will also explain the connection toclosely related independent work of Mautner-Riche.

♣ Tomoyuki Arakawa (Kyoto University)Joseph ideals and lisse minimal W-algebras (July 2, 9:40-10:35)

Motivated by a recent work of Kawasetu, we consider a lifting of Joseph ideals for minimalnilpotent orbit closures to the setting of affine Kac-Moody algebras, and find new examples of affinevertex algebras whose associated varieties are minimal nilpotent orbit closure. As an applicationwe obtain a new family of lisse (C2-cofinite) W- algebras that are not coming from admissiblerepresentation of affine Kac-Moody algebras.

♣ Shun-Jen Cheng (Academia Sinica)Finite-dimensional representations of the queer Lie superalgebra of half-integer weights(July 3, 14:00-14:55)

We give an interpretation of the representation theory of the finite-dimensional modules of thequeer Lie superalgebra of half-integer weights in terms of Brundan’s work of finite-dimensionalmodules of integer weights by means of Lusztig’s canonical basis. Using this new viewpoint wecompute the characters of the finite-dimensional irreducible modules of half-integer weights. In thespecial cases of irreducible modules whose highest weights are either totally connected and totallydisconnected we derive close for formulas for them that are reminiscent of Kac-Wakimoto characterformula for classical Lie superalgebras. This is a joint work with Jae-Hoon Kwon.

♣Weideng Cui (Tsinghua University)Affine cellularity of some infinite-dimensional algebras (July 4, 16:30-17:25)

Koenig and Changchang Xi recently defined the notion of affine cellularity, which generalizesthe notion of cellular algebras and provides a unified framework for studying the classification ofthe irreducible representations of algebras that do not need to be finite dimensional over a noethe-rian domain k. In this talk, we will show that Beck-Lusztig-Nakajima (BLN) algebras and affinequantum Schur algebras are affine cellular. Applying Koenig and Xi’s approach, we also study thehomological properties of these algebras.

♣ Chongying Dong (UC Santa Cruz)On orbifold theory (July 3, 8:30-9:25)

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that VG

is regular. It is proved that every irreducible VG-module occurs in an irreducible g-twisted V-modulefor some g ∈ G. Moreover, the quantum dimensions of each irreducible VG-module is determinedand a global dimension formula for V in terms of twisted modules is obtained.

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1.3 Abstracts of Workshop Talks 1 WORKSHOP

♣ Jie Du (University of New South Walse)Quantum linear supergroups and their canonical bases (July 3, 9:40-10:35)

It is well known that the most fundamental structure of a universal enveloping algebra associ-ated with a symmetrizable Kac-Moody algebra is stored in a matrix—the Cartan matrix. It is alsoknown that, if the associated Lie algebra is a matrix algebra, then a PBW basis is indexed by certainmatrices. In this talk, we will show that, in the type A family—the family of quantum linear group-s/supergroups and affine quantum linear groups—there is a new basis for every member of the family,which contains the set of generators, such that the structure constants associated with multiplyinga basis element by a generator are completely determined by the labeling matrices. This indicatesthat further structures of such an object are also stored in matrices. The first type of such bases wasconstructed for quantum linear groups two decades ago by Beilinson-Lusztig-MacPherson, using ageometric setting (i.e., the partial flag varieties) for q-Schur algebras. However, for the super andaffine cases, purely algebraic and combinatorial approaches have been developed. We will mainlyfocus on the construction of the quantum linear supergroups in the talk. By this new construction,we will also give a combinatorial construction for the canonical bases of the positive and negativeparts and discuss their relationship with the Kazhdan-Lusztig bases for the q-Schur superalgebrasand the induced bases for simple polynomial representations.

♣ Zhaobing Fan (Harbin Engineering University)Equivalence of representation categories of various quantum and super quantum groups(July 4, 15:10-4:05)

Corresponding to a Cartan datum, there are several versions of quantum enveloping algebras,including original quantum group in the form of Lusztig, and quantum groups with many parameters,as well as supervision. We establish equivalences of several representation theories of these quantumgroups under certain assumption by introducing a new multi-parameter quantum algebra and itsmodified form. This is a joint work with Yiqiang Li and Zongzhu Lin.

♣ Rolf Farnsteiner (Christian-Albrichits Universtitat Zu Kiel)Degrees of modules and varities of elementary abelian Lie algebras (July 4, 9:40-10:35)

Let (g; [p]) be a restricted Lie algebra over an algebraically closed field k. Work by Suslin-Friedlander-Bendel shows that the maximal ideal spectrum of the even cohomology ring H•(U0(g, k))of the restricted universal enveloping algebra is homeomorphic to the nullcone V(g) := {x ∈ g; x[p] =

0} of g. In a series of articles, Carlson, Friedlander, Pevtsova and Suslin have introduced full subcate-gories of U0(g)-modules, whose objects M are determined by properties of the p-nilpotent operators.A U0(g)-modules, whose objects M are determined by properties of the p-nilpotent operators

x jM : M → M; m 7→ x j.m (x ∈ V(g, j ∈ {1, · · · , p − 1}).

Given j ∈ {1, · · · , p − 1}, a U0(g)-module M is said to have constant j-rank, provided

rk(x jM)) = rk(y j

M) for all x, y ∈ V(g)\{0}.

These modules give rise to morphisms

im jM : P(V(g))→ Grd j (M); [x] 7→ imx j

M

from the projectivized nullcone into a Grassmannian. If g = cr is an elementary abelian Lie algebrasof dimension r ≥ 2, the above maps induce morphisms Pr−1 → Pn. In this talk, which is partly

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1.3 Abstracts of Workshop Talks 1 WORKSHOP

based on joint work with Hao Chang, we study the interplay between M and im jM and show how

the morphisms im jM may be used to define new invariants for such U0(g)-modules. The observation

that these invariants are determined by restricting modules to elementary abelian subalgebras ofdimension 2 motivates the investigation of the closed subset

E(2; g) := {c ∈ Gr2(g) is an elementary abelian p-subalgebra}

of the Grassmannian, which, in contrast to E(1; g) = P(V(g)), may not be connected.

♣ Cuipo Jiang (Shanghai Jiaotong University)Coset vertex operator algebras from tensor decomposition of affine vertex operator algebras(July 3, 11:00-11:55)

We will talk about some recent results on coset vertex operator algebras associated to affinevertex operator algebras.

♣ Jae-Hoon Kwon (Sungkyunkwan University)Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras (July 3, 16:30-17:55)

We give the classification of finite-dimensional tame modules over the ortho-symplectic Liesuperalgebras, and show that their characters are given by the Kac-Wakimoto character formula,thus establishing the Kac-Wakimoto conjecture for the ortho-symplectic Lie superalgebras. This isa joint work with Shun-Jen Cheng.

♣ Ivan Losev (Northeastern University)Quantizations of nilpotent orbits (July 2, 14:00-14:55)

I will explain some recent existence and uniqueness results for algebras of regular functionson nilpotent orbits and describe applications to computing the Goldie ranks of primitive ideals inuniversal enveloping algebras. The talk is based on http://arxiv.org/abs/1505.08048

♣ Satoshi Naito (Tokyo Institute of Technology)Specializations of symmetric Macdonald polynomials and pseudoQLS paths (July 4, 11:00-11:55)

A symmetric Macdonald polynomial Pλ(x; q, t) can be thought of as a certain graded characterof the crystal (for an affine Lie algebra) of pseudoQLS paths of shape λ; however, the representation-theoretic meaning of this (rather large) crystal is not yet known. In this talk, I explain that thespecialization Pλ(x; q, 0) at t = 0 of the symmetric Macdonald polynomial Pλ(x; q, t) is identical toa graded character of a canonical quotient W(λ) of a special Demazure submodule (correspondingto the longest element w0 of the finite Weyl group) of the level- zero extremal weight module ofextremal weight λ over a quantum affine algebra. Also, I would like to explain that the specializationEw0λ(x; q,∞) at t = ∞ of the nonsymmetric Macdonald polynomial Ew0λ(x; q, t) can be described asanother graded character of the (same) canonical quotient W(λ) above, but with a curious gradingdifferent from the one in the t = 0 case.

♣ Peng Shan (CNRS researcher, University of Paris-Sud)On the center of quiver Hecke algebras (July 2, 11:00-11:55)

I will explain how to relate the center of a cyclotomic quiver Hecke algebras to the cohomologyof Nakajima quiver varieties using a current algebra action. This is a joint work with M. Varagnoloand E. Vasserot.

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1.3 Abstracts of Workshop Talks 1 WORKSHOP

♣ Toshiaki Shoji (Tongji University)Springer correspondence for complex reflection groups and related Kostka functions(July 2, 8:30-9:25)

Let V be a 2n-dimensional vector space over an algebraically closed field of odd characteristic.Put G = GL(V) and H = S p(V), and consider the symmetric space G/H. A variety X = G/H ×Vr−1

is called an exotic symmetric space of level r. Similarly, for an n-dimensional vector space V , weconsider the variety X = GL(V) × Vr−1, which is called an enhanced variety of level r. For eithercase, one can define the unipotent subvariety X0 of X.

Let W = Wn,r be the complex reflection group defined as a semi direct product of the symmetricgroup S n and the cyclic group (Z/rZ)n. In this talk, we show that there exists a natural bijectivecorrespondence between the set of irreducible representations of W and a certain set of intersectioncohomologies arising from X0 of exotic type.

A similar correspondence also holds in the case of the enhanced variety, in a reduced form.Kostka functions associated to complex reflection groups are functions indexed by pairs of r-tupleof partitions, which is an analogue of the original Kostka polynomials indexed by pairs of partitions.It is expected, as in the classical case, that those Kostka functions are closely related to the geometryof X0 (for both type). We will explain some results, in the case of enhanced type, supporting thisconjecture.

♣ Jinkui Wan (Beijing Institute of Technology)Frobenius map for the centers of Hecke algebras (July 2, 15:10-16:05)

We introduce a commutative associative graded algebra structure on the direct sum Z of thecenters of the Hecke algebras associated to the symmetric groups in n letters for all n. As a naturaldeformation of the classical construction of Frobenius, we establish an algebra isomorphism fromthe algebra Z to the ring of symmetric functions. This isomorphism provides an identification be-tween several distinguished bases for the centers (introduced by Geck-Rouquier, Jones, Lascoux)and explicit bases of symmetric functions. This is a joint work with Weiqiang Wang.

♣Weiqiang Wang (University of Virginia)Canonical bases for tensor product modules (July 3, 15:10-16:05)

We will explain the construction of canonical bases in tensor products of several lowest andhighest weight integrable modules (and a theory of based modules for general quantum groups),generalizing Lusztig’s work. This is joint work with Huanchen Bao.

♣ Nanhua Xi (Chinese Academy of Science)Representations in rational functions (July 4, 8:30-9:25)

Representations in polynomials have been investigated for long time and are pretty well under-stood, although there are still many problems to be settled. It seems that representations in rationalfunctions are not much studied. In this talk we will give some discussions to representations inrational functions.

♣ Yang Zeng (Nanjing Audit University)Finte W-superalgebras for basic Lie superalgebras and their applications (July 2, 16:30-17:25)

In this talk we mainly consider the related topics on finite W-superalgebra U(gF, e) for a basicLie superalgebra gF = (gF)0 + (gF)1 associated with a nilpotent element e ∈ (gF)0 both over the fieldof complex numbers F = C and over F = K an algebraically closed field of positive characteristic.

8

1.3 Abstracts of Workshop Talks 1 WORKSHOP

In the first part, we present the PBW theorem for U(gF, e). In contrast with finite W-algebras,one can find that the construction of U(gF, e) is divided into two cases in virtue of the parity ofdim(gF(−1)1).

A module of gK is said to be of Kac-Weisfeiler type if its dimension coincides with the one inthe super Kac-Weisfeiler property presented by Wang-Zhao, which is the dimensional lower boundfor the modular representations of a basic Lie superalgebra gK over an algebraically closed fieldK of positive characteristic p. In the second part, we verify the existence of the Kac-Weisfeilermodules for glm|n over an algebraically closed field Fp of characteristic p > 2. We also establish thecorresponding consequence for slm|n with restrictions p > 2 and p - (m − n).

In the third part, we formulate a conjecture about the minimal dimensional representationsof the finite W-superalgebra U(gC, e) over the field of complex numbers and demonstrate it withexamples including all the cases of type A. Under the assumption of this conjecture, we verify theexistence of the modules of Kac-Weisfeiler type for any basic Lie superalgebras in characteristicp � 0.

This talk is joint work with Bin Shu.

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2 SUMMER SCHOOL

2 Summer School

2.1 Lecturers

Ac = Pramod N. Achar (8 Lectures for the first period + 16 Lectures for the second period)

Lo = Ivan Losev (8 Lectures)

Sh = Peng Shan (8 Lectures)

Wa = Weiqiang Wang (8 Lectures)

2.2 Schedule of Mini-Courses in the Summer School

Jun.28 – 28 29 30 1 6 7 8 9 13 14 15 16 17 20 21 22

Jul.22 Sun. Mon. Tue. Wed. Mon. Tue. Wed. Thu. Mon. Tue. Wed. Thu. Fri. Mon. Tue. Wed

9:30-10:25 Sh Sh Sh Wa Wa Wa Wa Ac Ac Ac Ac Ac Ac Ac Ac

10:45-11:40 Sh Sh Sh Wa Wa Wa Wa Ac Ac Ac Ac Ac Ac Ac Ac

13:30-14:25 Sh Lo Lo Lo Ac Ac Ac Ac Q&A Q&A Q&A Q&A Q&A Q&A Q&A Q&A

14:45-15:40 Sh Lo Lo Lo Ac Ac Ac Ac CT

16:00-16:55 Q&A Q&A Lo Lo Q&A Q&A Q&A Q&A CT

18:30-19:30 Q&A Q&A

Lecture Room 2-108 4-111 4-111 4-115 4-111 4-111 4-111 4-202 2-109 2-109 2-109 2-109 1-107 1-111 1-111 1-111

• 2-108/109 = Teaching Building No.2 108/109 (1��Æ¢ 108/109)

• 4-111/202 = Teaching Building No.4 111/202 (1o�Æ¢ 111/202)

• 1-107/111 = Teaching Building No.1 107/111 (1��Æ¢ 107/111)

• CT= Contributed Talks

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2.3 Descriptions of Mini-Courses in the Summer School 2 SUMMER SCHOOL

2.3 Descriptions of Mini-Courses in the Summer School

Quiver Hecke algebras and applicationsby Pang Shan (8 lectures)

Quiver Hecke algebras have been introduced independently by Khovanov-Laudaand Rouquier to study categorifications of Kac-Moody algebras. Among other-s, they have found important applications in the study of representations of Kac-Moody algebras, Hecke algebras, Cherednik algebras, quantum affine algebras, andfinite groups of Lie type. From a geometric perspective, these algebras can beviewed as extension algebras of some perverse sheaves, and are closely related toLusztig’s canonical bases and the geometry of Nakajima quiver varieties. The goalof this course is to give an introduction to these algebras together with some of theapplications mentioned above.

Rational Cherednik algebrasby Ivan Losev (8 lectures)

Rational Cherednik algebras were introduced by Etingof and Ginzburg.Theyhave interesting and rich representation theory and have connections to many otherparts of mathematics: integrable systems, Algebraic geometry, combinatorics, knottheory. In these lectures I will introduce their algebras, discuss their structure andrepresentation theory and also review some of connections mentioned above.

Quantum (super) groups and canonical basesby Weiqiang Wang (8 lectures)

We will give an introduction to (a class of ) quantum supergroups and canonicalbases. This (so-called anisotropic type) class of quantum supergroups has complete-ly analogous structures and representation theory as for the Drinfeld-Jimbo quan-tum groups. Indeed, we shall discuss all these in a framework of quantum coveringgroups with a usual quantum parameter q together with a new parameter p whichsquares to 1. We shall construct canonical bases of the quantum covering groups.The specializations of quantum covering groups at p = 1 and p = −1 are quantumgroups and supergroups, respectively. Time permitting, we shall discuss in the endthe categorification of the rank one covering group using spin nilHecke algebras.

Perverse sheaves in representation theoryby Pramod N. Achar (8 lectures)

This mini-course will discuss what perverse sheaves are, how to work withthem, and why they come up in representation theory. Examples will include

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2.4 Contributed Talks 2 SUMMER SCHOOL

Kazhdan-Lusztig theory, Springer theory/character sheaves, and the geometric Sa-take equivalence. The second half will focus in more detail on Springer theory andcharacter sheaves, with some discussion of recent developments in positive charac-teristic.

Modular perverse sheaves on flag varieties and representations of algebraicgroups

by Pramod N. Achar(16 lectures for the second period of summer school)

This mini-course will begin with background on the representation theory ofalgebraic groups in positive characteristic, and its various geometric incarnations,with a focus on Soergel’s work connecting it to modular perverse sheaves on flagvarieties. The second half of the course will be devoted to recent developments,such as the discovery of torsion by Braden and He-Williamson, and the role ofKoszul duality and its generalizations.

2.4 Contributed Talks

Canonical bases for the quantum supergroups U(glm|n)

—by Haixia Gu (Huzhou Normal University)

Abstract: We give a combinatorial construction for the canonical bases of the ±-parts of the quan-tum enveloping superalgebra U(glm|n) and discuss their relationship with the Kazhdan-Lusztig basesfor the quantum Schur superalgebras S(m|n, r) introduced in [DR]. We will also extend this relation-ship to the induced bases for simple polynomial representations of U(glm|n). This is the joined workwith Jie Du.

Decomposition of the Kazhdan-Lusztig basis

—By Xun Xie (Chinese Academy of Science)

Abstract: In this short talk, I will try to present some partial results on the decomposition ofKazhdan-Lusztig basis of Hecke algebras. We can confirm this kind of decomposition formulafor

• the lowest two-sided cell of an affine Hecke algebra with unequal parameters;

• affine Hecke algebras of rank 2 with positive parameters;

• Hecke algebras of type A, and hence of type A.

This kind of decomposition will be useful for understanding the representations of Hecke algebras.For example, we can see from this kind of decomposition formula that the Kazhdan-Lusztig basis ofHecke algebras of type A (resp. A) is a (resp. affine) cellular basis.

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3 PARTICIPANTS

3 Participants

Name Affiliation

Shun-Jen Cheng£§_;¤ Academia Sinica£¥ïÄ�¤

Xinfeng Liang£ù#¸¤ Beijing Institute of Technology£�®nó�Ƥ

Jinkui Wan£�7¿¤ Beijing Institute of Technology£�®nó�Ƥ

Kai Zhou£±p¤ Beijing Institute of Technology£�®nó�Ƥ

Pan Chen£��¤ Chinese Academy of Sciences£¥��êÆ�XÚ�ÆïÄ�¤

Xiaoyu Chen£�¡ø¤ Chinese Academy of Sciences£¥��êÆ�XÚ�ÆïÄ�¤

Junbin Dong£ÂdR¤ Chinese Academy of Sciences£¥��êÆ�XÚ�ÆïÄ�¤

Jianwei Gao£pê�¤ Chinese Academy of Sciences£¥��êÆ�XÚ�ÆïÄ�¤

Yue Hu£��¤ Chinese Academy of Sciences£¥��êÆ�XÚ�ÆïÄ�¤

Sian Nie£mgS¤ Chinese Academy of Sciences£¥��êÆ�XÚ�ÆïÄ�¤

Nanhua Xi£RHu¤ Chinese Academy of Sciences£¥��êÆ�XÚ�ÆïÄ�¤

Xun Xie£�פ Chinese Academy of Sciences£¥��êÆ�XÚ�ÆïÄ�¤

Rolf Farnsteiner Christian-Albrichits Universitat Zu Kiel

Peng Shan£üC¤ CNRS researcher, University of Paris-Sud

Min Cao£ù¯¤ East China Normal University£uÀ���Ƥ

Hao Chang£~Ó¤ East China Normal University£uÀ���Ƥ

Miaofen Chen£�¢¥¤ East China Normal University£uÀ���Ƥ

Changjie Cheng£¤~#¤ East China Normal University£uÀ���Ƥ

Wenzhe Fu£L©)¤ East China Normal University£uÀ���Ƥ

Mengmeng Gao£p��¤ East China Normal University£uÀ���Ƥ

Ziyu Guo£HfÕ¤ East China Normal University£uÀ���Ƥ

Hongmei Hu (�ùr) East China Normal University£uÀ���Ƥ

Naihong Hu£�Dù¤ East China Normal University£uÀ���Ƥ

Yan Hu£�ó¤ East China Normal University£uÀ���Ƥ

Xiangyu Jiao (���) East China Normal University£uÀ���Ƥ

Haibo Jin£A°Å¤ East China Normal University£uÀ���Ƥ

Sichen Li£og�¤ East China Normal University£uÀ���Ƥ

Jie Liu£4#¤ East China Normal University£uÀ���Ƥ

Li Luo (Ûv) East China Normal University£uÀ���Ƥ

Weiguo Lv (½�I) East China Normal University£uÀ���Ƥ

Fangfang Ma£ê��¤ East China Normal University£uÀ���Ƥ

Lei Pan£�[¤ East China Normal University£uÀ���Ƥ

Zihao Qi£àfͤ East China Normal University£uÀ���Ƥ

13

3 PARTICIPANTS

Dejing Rui£��·¤ East China Normal University£uÀ���Ƥ

Hebing Rui£�ÚW¤ East China Normal University£uÀ���Ƥ

Jianyi Shi£�|ä East China Normal University£uÀ���Ƥ

Bin Shu£ÓR¤ East China Normal University£uÀ���Ƥ

Dan Wang£�û¤ East China Normal University£uÀ���Ƥ

Jianpan Wang£�ï�¤ East China Normal University£uÀ���Ƥ

Xin Wen£§!¤ East China Normal University£uÀ���Ƥ

Husileng Xiao£��de¤ East China Normal University£uÀ���Ƥ

Rongchuan Xiong£=JA¤ East China Normal University£uÀ���Ƥ

Jinyi Xu£M7⤠East China Normal University£uÀ���Ƥ

Yunpeng Xue£Å�+¤ East China Normal University£uÀ���Ƥ

Nana Yan£AAA¤ East China Normal University£uÀ���Ƥ

Gao Yang£ p¤ East China Normal University£uÀ���Ƥ

Hanyang You£c¿�¤ East China Normal University£uÀ���Ƥ

Xiaoting Zhang£Ü�x¤ East China Normal University£uÀ���Ƥ

Ying Zheng£x=¤ East China Normal University£uÀ���Ƥ

Guodong Zhou (±IÅ) East China Normal University£uÀ���Ƥ

Kun Zhou£±%¤ East China Normal University£uÀ���Ƥ

Zhaobing Fan (�ëW) Harbin Engineering University£M�Tó§�Ƥ

Qi Wang£�l¤ Harbin Institute of Techonlogy£M�Tó��Ƥ

Shujuan Wang£�Ôï¤ Harbin Institute of Techonlogy£M�Tó��Ƥ

Yang Liu£4�¤ Harbin Normal University£M�T���Ƥ

Qiang Mu (;r) Harbin Normal University£M�T���Ƥ

Liming Tang£/i²¤ Harbin Normal University£M�T���Ƥ

Yong Yang£ ]¤ Harbin Normal University£M�T���Ƥ

Haixia Gu£�°_¤ Huzhou Normal University�²��Æ�)

Hui Chen£�¦¤ Kansas State University (sid²á�Æ)

Tomoyuki Arakawa Kyoto University

Qianqian Zhang£ÜÊʤ Lanzhou University£=²�Ƥ

Pramod N. Achar Louisiana State University

Yang Zeng£Q�¤ Nanjing Audit University£H®"OÆ�¤

Jianjian Jiang£öêê¤ Nankai University£Hm�Ƥ

Yiyi Zhu£Á½²¤ Nankai University£Hm�Ƥ

Yung-Ning Peng£$]w¤ National Central University£Iá¥�A¤

Yuling Wu£Ç� ¤ Northeast Normal University£À����Ƥ

Ivan Losev Northeastern University

14

3 PARTICIPANTS

Euiyong Park Seoul National University

Zhaojia Tong£éîZ¤ Shanghai Dianji University£þ°>ÅÆ�¤

Cuipo Jiang£ñ}Ť Shanghai Jiaotong University£þ°�Ï�Ƥ

Yufeng Yao£�ü´¤ Shanghai Maritime University£þ°°¯�Ƥ

Linliang Song£y��¤ Shanghai Normal University£þ°���Ƥ

Jiao Zhang£Üd¤ Shanghai University£þ°�Ƥ

Li Ren£?w¤ Sichuan University£oA�Ƥ

Jae-Hoon Kwon Sungkyunkwan University

Chih-Whi Chen£=�&¤ Taiwan University£���Ƥ

Satoshi Naito Tokyo Institute of Technology

Haibo Chen£�°Å¤ Tongji University£ÓL�Ƥ

Qiufan Chen£�¢~¤ Tongji University£ÓL�Ƥ

Xiansheng Dai£�k�¤ Tongji University£ÓL�Ƥ

Wenting Gao£p©x¤ Tongji University£ÓL�Ƥ

Jianzhi Han£¸ï�¤ Tongji University£ÓL�Ƥ

Juanjuan Li£oïï¤ Tongji University£ÓL�Ƥ

Shiyuan Liu£4��¤ Tongji University£ÓL�Ƥ

Xiao Liu£4�¤ Tongji University£ÓL�Ƥ

Toshiaki Shoji Tongji University£ÓL�Ƥ

Bo Yu£{Ť Tongji University£ÓL�Ƥ

Weideng Cui£w��¤ Tsinghua Univesity£�u�Ƥ

Chongying Dong£ÂÂ=¤ UC Santa Cruz

Xiao He£Û�¤ UniversitW Laval§Canada

Jie Du£Ú#¤ University of New South Wales

Michael Alan Reeks Jr University of Virginia

Chun-Ju Lai£�dV¤ University of Virginia

Weiqiang Wang£��r¤ University of Virginia

Fei Kong£��¤ Xiamen University£f��Ƥ

Ming Li£o²¤ Xiamen University£f��Ƥ

Zhiqiang Li£o�r¤ Xiamen University£f��Ƥ

Feifei Duan£à��¤ Zhejiang University£úô�Ƥ

Yan Tan£ ý¤ Zhejiang University£úô�Ƥ

15

4 INFORMATION

4 Information

1. The Lecture Notes of all lectures and of all talks will be collected and put on the webpage.

2. Email Rooms: 200A#, the second floor, Department of Mathematics. The open time will beannounced later.

3. Printer Room: 236# Department of Mathematics.

4. Group Photos for Workshop: We will take a group photo of all participants in front of theLibrary after talks in the morning section of Thursday (July 2)

5. Cafeteria:

• Huamin Cafeteria (near Teaching Buildings No.1 and No.2; ����NC�uDêe;

• Qiushige Cafeteria (near Department of Mathematics¶êÆXNC�¢¢�;

• Qiulinge Cafeteria (inside the district of graduate lodging¶ïÄ)úû¢��.

6. Introduction to tourism and entertainments:

• The Bond, including the World Architecture at the Bond, Huang Pu River Cruise in the evening.

• Shanghai History Museum, including the People’s Square, Nanjing Road Walk Street.

• Beijing Opera or Hangzhou Opera (Yue Opera) in Shanghai Grand Theater, Shanghai Music The-ater or Pudong Oriental Theater.

• Shanghai Old Town (including Yuyuan Gardon, Old City God Temple. Yuyuan Commercial City)

• Some other recommendable tour sites:

– Qibao old town£Ô��¤

– Tianzifang£Xf�¤

– Xintiandi£#U/, a shopping, eating and entertainment area of Shanghai, with webpagehttp://www.xintiandi.com¤.Add: South Huangpi Road, near Madang RoadPublic transport: The closest metro stationto Xintiandi is South Huangpi Rd., on Metro Line No.1, walking down South Huangpi Rd.or Madang Rd. for about 5 minutes.

(For more entertainment and tourism information, you can learn from the webpage http://www.meet-in-shanghai.net/)

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