Canonical bases and the conjugating representation of a semisimple group

Abstract

Let G be a semisimple simply connected affine algebraic group over an algebraically closed field k of characteristic zero, let A(G) be the k-algebra of regular functions of G, and let C(G) be the subalgebra consisting of class functions. We explain how Lusztig's work on canonical bases affords a constructive proof of the fact, due to Richardson, that A(G) is a free C(G)-module.