The q-Schur Algebra

This book focuses on the representation theory of q-Schur algebras.

S. Donkin (Author)

9780521645584, Cambridge University Press

Paperback, published 10 December 1998

192 pages
22.8 x 15.3 x 1.2 cm, 0.275 kg

"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

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.

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.

Subject Areas: Applied mathematics [PBW], Algebra [PBF]