Representation Theory of Iwahori-Hecke Algebras and Schur Algebras of Symmetric Groups

Abstract

In this thesis, we study the modular representation theory of the Iwahori-Hecke algebra H and the q-Schur algebra S of the symmetric group. The Iwahori-Hecke algebra of the symmetric group is a one-parameter deformation of the group algebra of a symmetric group, and it is hoped that a detailed study of its modular representation theory will reveal to us valuable information about the modular representations of the symmetric groups. We will first introduce the theory of cellular algebras, and apply it to classify the irreducible H-modules and S-modules.