Fusion procedure for wreath products of finite groups by the symmetric group

TL;DR

This paper introduces a fusion procedure to construct a complete system of orthogonal idempotents for wreath products of finite groups with the symmetric group, using rational functions and Young multi-tableaux.

Contribution

It develops a novel fusion procedure for wreath products, incorporating Baxterized Artin generators and indexing by Young multi-tableaux.

Findings

Constructed a complete system of orthogonal idempotents

Defined a Baxterized form for Artin generators

Applied the fusion procedure to wreath products

Abstract

Let G be a finite group. A complete system of pairwise orthogonal idempotents is constructed for the wreath product of G by the symmetric group by means of a fusion procedure, that is by consecutive evaluations of a rational function with values in the group ring. This complete system of idempotents is indexed by standard Young multi-tableaux. Associated to the wreath product of G by the symmetric group, a Baxterized form for the Artin generators of the symmetric group is defined and appears in the rational function used in the fusion procedure.