Modular Representation Theory of Finite Groups

by Collins, Michael J.; Parshall, Brian; Scott, Leonard L.

• ISBN13: 9783110163674
• ISBN10: 3110163675
• Format: Hardcover
• Copyright: 2001-10-01
• Publisher: De Gruyter

Summary

This book is an outgrowth of a Research Symposium on the Modular Representation Theory of Finite Groups, held at the University of Virginia in May 1998. The main themes of this symposium were representations of groups of Lie type in nondefining (or cross) characteristic, and recent developments in block theory. Series of lectures were given by M. Geck, A. Kleshchev and R. Rouquier, and their brief was to present material at the leading edge of research but accessible to graduate students working in the field. The first three articles are substantial expansions of their lectures, and each provides a complete account of a significant area of the subject together with an extensive bibliography. The remaining articles are based on some of the other lectures given at the symposium; some again are full surveys of the topic covered while others are short, but complete, research articles. The opportunity has been taken to produce a book of enduring value so that this is not a conference proceedings in the conventional sense. Material has been updated so that this book, through its own content and in its extensive bibliographies, will serve as an invaluable resource for all those working in the area, whether established researchers or graduate students who wish to gain a general knowledge of the subject starting from a single source.

Table of Contents

Preface	v
Lectures given during the Symposium	ix
Modular Harish-Chandra series, Hecke algebras and (generalized) q-Shur algebras	1	(66)
Meinolf Geck
Tensor Products and restrictions in type A	67	(34)
Jonathan Brundan
Alexander S. Kleshchev
Block theory via stable and Rickard equivalences	101	(46)
Raphael Rouquier
Alperin's weight conjecture in terms of linear source modules and trivial source modules	147	(10)
Robert Boltje
Alvis--Curtis duality as an equivalence of derived categories	157	(18)
Marc Cabanes
Jeremy Rickard
Relating the cohomology of general linear groups and symmetric groups	175	(14)
Stephen R. Doty
Daniel K. Nakano
Generalized q-Schur algebras and the ways to approach them	189	(22)
Jie Du
Filtrations on projective modules for Iwahori--Hecke algebras	211	(12)
Meinolf Geck
Raphael Rouquier
Projective representations for some exceptional finite groups of Lie type	223	(8)
Corneliu Hoffman
Splitting fields and twisted group rings for the finite general linear groups	231	(8)
Nicholas J. Kuhn
Irreducible tensor products of representations of finite quasi-simple groups of Lie type	239
Kay Maagard
Pham Huu Tiep