Fusion procedure for Coxeter groups of type B and complex reflection groups G(m,1,n)

TL;DR

This paper develops a method to explicitly construct orthogonal idempotents for Coxeter groups of type B and complex reflection groups G(m,1,n) using evaluations of rational functions related to Jucys--Murphy elements.

Contribution

It introduces a complete system of primitive orthogonal idempotents for these groups via a novel evaluation technique involving rational functions.

Findings

Explicit construction of primitive orthogonal idempotents

Application to Coxeter groups of type B and G(m,1,n)

Method based on evaluations of rational functions

Abstract

A complete system of primitive pairwise orthogonal idempotents for the Coxeter groups of type $B$ and, more generally, for the complex reflection groups $G(m,1,n)$ is constructed by a sequence of evaluations of a rational function in several variables with values in the group ring. The evaluations correspond to the eigenvalues of the two arrays of Jucys--Murphy elements.