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The q-Schur Algebra S. Donkin (Queen Mary University of London)

The q-Schur Algebra By S. Donkin (Queen Mary University of London)

Summary

Using a largely homological approach, this book focuses on the representation theory of q-Schur algebras and connections with the representation theory of Hecke algebras and quantum general linear groups. It will be primarily of interest to researchers in algebra and related topics in pure mathematics.

The q-Schur Algebra Summary

The q-Schur Algebra by S. Donkin (Queen Mary University of London)

This book focuses on the representation theory of q-Schur algebras and connections with the representation theory of Hecke algebras and quantum general linear groups. The aim is to present, from a unified point of view, quantum analogues of certain results known already in the classical case. The approach is largely homological, based on Kempf's vanishing theorem for quantum groups and the quasi-hereditary structure of the q-Schur algebras. Beginning with an introductory chapter dealing with the relationship between the ordinary general linear groups and their quantum analogies, the text goes on to discuss the Schur Functor and the 0-Schur algebra. The next chapter considers Steinberg's tensor product and infinitesimal theory. Later sections of the book discuss tilting modules; the Ringel dual of the q-Schur algebra; Specht modules for Hecke algebras; and the global dimension of the q-Schur algebras. An appendix gives a self-contained account of the theory of quasi-hereditary algebras and their associated tilting modules. This volume will be primarily of interest to researchers in algebra and related topics in pure mathematics.

The q-Schur Algebra Reviews

This is a well-written book which should be accessible to a graduate student with a background in homological algebra. It will be of particular interest to researchers working on the representation theory of the general linear group and quantum groups. Proceedings of the Edinburgh Mathematical Society

Table of Contents

Introduction; 1. Exterior algebra; 2. The Schur functor and a character formula; 3. Infinitesimal theory and Steinberg's tensor product theorem; 4. Further topics; References; Appendix.

Additional information

NLS9780521645584
9780521645584
0521645581
The q-Schur Algebra by S. Donkin (Queen Mary University of London)
New
Paperback
Cambridge University Press
1998-12-10
192
N/A
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