Representations of Yokonuma--Hecke algebras

TL;DR

This paper computes specific character values of Yokonuma--Hecke algebras at key elements, advancing understanding of their representation theory using classical methods.

Contribution

It provides explicit character value computations for Yokonuma--Hecke algebras at particular Weyl group elements, a novel application of classical representation theory techniques.

Findings

Computed character values at $w_{0}$ and $w_{0}^{2}$

Enhanced understanding of Yokonuma--Hecke algebra representations

Applied classical representation theory to new algebraic contexts

Abstract

The Iwahori--Hecke and Yokonuma--Hecke algebras have played crucial roles in algebraic combinatorics and the representation theory of finite groups. In this work, we use classical results from representation theory to compute the character values of the Yokonuma--Hecke algebra at $w_{0}$ and $w_{0}^{2}$, where $w_{0}$ denotes the element of maximal length in the corresponding Weyl group.