Topics in Cotnputational Algebra

Edited by

G. M. PIACENTINI CATIANEO

and

E. STRICKLAND Department of Mathematics, University of Rome Il 'Tor Vergata', ltaly

Reprinted from Acta Applicandae Mathematicae, Volume 21, Nos. 1 & 2 (1990)

SPRINGER SCIENCE+BUSINESS MEDIA, B.V.

Library of Congress Cataloging in Publication Data

Topies in eomputational algebra / edited by G.M. Piaeentini Cattaneo, E. Striekland

p. cm. "Papers presented at the Computational Algebra Seminar held at the

University of Rome 'Tor Vergata,' 9-11 May 1990"--P. "Acta appllcandae mathematicae, volume 21, nas. 1 and 2,

October/November 1990"--P. rSBN 978-94-0l0-5514-7 ISBN 978-94-011-3424-8 (eBook) DOI 10.1007/978-94-011-3424-8 1. Algebra--Data processing--Congresses. r. Piaeentini Cattaneo, G. M.

II. Strickland, E. (Elisabetta), 1948- III. Computational Algebra Seminar (1990 University of Rome "Tor Vergata") QAI55.7.E4T67 1990 512' .0028--dc20

ISBN 978-94-010-5514-7

Printed an acid-free paper

AII Rights Reserved © 1990 by Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1990 Softcover reprint of the hardcover 1 st edition 1990

90-27032

No part of the material protected by this copyright notice may be reproduced or utilized in any fonn or by any means, electronic or mechanical, including photocopying, recording or by any infonna­tion storage and retrieval system, without written pennission from the copyright owner.

Contents

G. M. PIACENTINI CATTANEO and E. STRICKLAND / Foreword

V. G. KAC and M. WAKIMOTO / Branching Functions for Winding Subalgebras and Tensor Products 3

H. P AHLINGS / Computing with Characters of Finite Groups 41

F. CELLER, J. NEUBUSER, and C. R. B. WRIGHT / Some Remarks on the Computation of Complements and Normalizers in Soluble Groups 57

MIKE STILLMAN / Methods for Computing in Algebraic Geometry and Com-mutative Algebra 77

JEFFREY B. REMMEL / Combinatorial Algorithms for the Expansion of Various Products of Schur Functions 105

VESSELIN DRENSKY / Polynomial Identities for 2 x 2 Matrices 137

NEIL L. WHITE / Cayley Factorization and a Straightening Algorithm 163

EDWARD FORMANEK / The Nagata-Higman Theorem 185

ROSA Q. HUANG, GIAN-CARLO ROTA, and JOEL A. STEIN / Supersym-metric Bracket Algebra and Invariant Theory 193

DA VID A. BUCHSBAUM / Aspects of Characteristic-Free Representation Theory of GLI!' and Some Applications to Intertwining Numbers 247