IwahoriHecke algebras and Schur algebras of the symmetric groupAndrew MathasUniversity lecture series, 15, American Mathematical Society (Providence, R.I.), 1999.MR 2001g:20006


Key wordsIwahoriHecke algebras, qSchur algebras, cellular algebras.
AbstractThis volume presents a fully selfcontained introduction to the modular representation theory of the IwahoriHecke algebras of the symmetric groups and of the qSchur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems.The main results are proved by showing that the IwahoriHecke algebras and qSchur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in Chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the qSchur algebras. This book is the first of its kind covering the topic. It offers a substantially simplified treatment of the original proofs. The book is a solid reference source for experts. It will also serve as a good introduction to students and beginning researchers since each chapter contains exercises and there is an appendix containing a quick development of the representation theory of algebras. A second appendix gives tables of decomposition numbers.
Table of contents
ISBN 0821819267. 211 pages. AMS Subject Classification (1991)Primary: 20C30, 16G99Secondary: 05E10, 20G05, 20C20
Andrew Mathas 