Bulletin of the Australian Mathematical Society

Research Article

Representations of Weyl groups of type B induced from centralisers of involutions

Philip D. Ryana1

a1 Department of Mathematics, IAS ANU, GPO Box 4 Canberra ACT 2601, Australia

Abstract

Let G be a Weyl group of type B, and T a set of representatives of the conjugacy classes of self-inverse elements of G. For each t in T, we construct a (complex) linear character πt of the centraliser of t in G, such that the sum of the characters of G induced from the πt contains each irreducible complex character of G with multiplicity precisely 1. For Weyl groups of type A (that is, for the symmetric groups), a similar result was published recently by Inglis, Richardson and Saxl.

(Received November 26 1991)