Canonical bases and the conjugating representation of a semisimple group

Pierre Baumann

Vol. 206 (2002), No. 1, 25–37

DOI: 10.2140/pjm.2002.206.25

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.

Milestones

Received: 28 December 2000

Published: 1 September 2002