Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T03:19:07.582Z Has data issue: false hasContentIssue false

Seminormal representations of Weyl groups and Iwahori-Hecke algebras

Published online by Cambridge University Press:  01 July 1997

Get access

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 $A_n$, $B_n$, $D_n$, $G_2$. Although these computations are in reach for types $F_4$, $E_6$ and $E_7$, we shall postpone this to another work.

1991 Mathematics Subject Classification: primary 20F55, 20C15; secondary 20C30, 20G05.

Type
Research Article
Copyright
London Mathematical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)