The q-Schur algebra - Donkin, Stephen (Cambridge University Press, 1998)
Title from PDF title page (viewed on Apr. 9, 2013). - "Transferred to digital printing 2006."
Includes bibliographical references (p. [165]-170) and indexes
Ch. 0 - Introduction -- - Ch. 1 - Exterior algebra -- - Ch. 2 - The Schur Functor and a Character Formula -- - Ch. 3 - Infinitesimal Theory and Steinberg's Tensor Product Theorem -- - Ch. 4 - Further Topics -- - App - Quasihereditary Algebras
This book focusses 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 quasihereditary structure of the q-Schur algebras