Seminormal representations of Weyl groups and Iwahori-Hecke algebras

Abstract

The purpose of this paper is to describe a general procedure for computing analogues of Young's seminormal representations of the symmetric groups. The method is to generalize the Jucys‐Murphy elements in the group algebras of the symmetric groups to arbitrary Weyl groups and Iwahori‐Hecke algebras. The combinatorics of these elements allows one to compute irreducible representations explicitly and often very easily. In this paper we do these computations for Weyl groups and Iwahori‐Hecke algebras of types An, Bn, Dn, G2. Although these computations are in reach for types F4, E6 and E7, we shall postpone this to another work. 1991 Mathematics Subject Classification: primary 20F55, 20C15; sec..