TY - BOOK ID - 77895920 TI - The q-Schur algebra PY - 1998 SN - 1139885480 1107367646 1107372208 1107362733 1107369274 1299405266 110736518X 0511893515 0511600704 9781107362734 9780511893513 9780521645584 0521645581 9780511600708 PB - Cambridge : Cambridge University Press, DB - UniCat KW - Representations of groups. KW - Representations of algebras. KW - Group representation (Mathematics) KW - Groups, Representation theory of KW - Group theory KW - Algebra UR - https://www.unicat.be/uniCat?func=search&query=sysid:77895920 AB - 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. ER -