Hecke algebras and Schur algebras of the symmetric group
Research Report 98-13
Date: 24 June 1998
Status: This report was a preliminary version of a
book published by the AMS.
These notes give a fully self-contained introduction to the (modular)
representation theory of the Iwahori-Hecke algebras and the q-Schur
algebras of the symmetric groups. The central aim of this work is to give
a concise, but complete, and an elegant, yet quick, treatment of the
classification of the simple modules and of the blocks of these two
important classes of algebras. Our approach is combinatorial in nature and
is based upon the construction of (cellular) bases which are particularly
well adapted to the representation theory.
Iwahori-Hecke algebras. q-Schur algebras. cellular algebras.
AMS Subject Classification (1991)
Primary: 20C30, 16G99
Secondary: 05E10, 20G05, 20C20
Sydney Mathematics and Statistics