Modular Representation Theory of Finite Groups

Proceedings of a Symposium held at the University of Virginia, Charlottesville, May 8-15, 1998

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

• Publisher: De Gruyter
• Year: 2011
• Print ISBN: 9783110163674
• eBook ISBN: 9783110889161
• Edition: 1
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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
• Lectures given during the Symposium
• Modular Harish-Chandra series, Hecke algebras and (generalized) q-Schur algebras
• Tensor products and restrictions in type A
• Block theory via stable and Rickard equivalences
• Alperin’s weight conjecture in terms of linear source modules and trivial source modules
• Alvis-Curtis duality as an equivalence of derived categories
• Relating the cohomology of general linear groups and symmetric groups
• Generalized q-Schur algebras and the ways to approach them
• Filtrations on projective modules for Iwahori-Hecke algebras
• Projective representations for some exceptional finite groups of Lie type
• Splitting fields and twisted group rings for the finite general linear groups
• Irreducible tensor products of representations of finite quasi-simple groups of Lie type