Fusion procedure for Yokonuma-Hecke algebras

TL;DR

This paper presents a method to explicitly construct a complete set of primitive idempotents for Yokonuma-Hecke algebras using evaluations of a rational function, advancing algebraic understanding of these structures.

Contribution

It introduces a fusion procedure that systematically produces primitive idempotents for Yokonuma-Hecke algebras, extending previous algebraic techniques.

Findings

Primitive idempotents obtained via rational function evaluations

Method provides a complete orthogonal set of idempotents

Advances algebraic tools for Yokonuma-Hecke algebras

Abstract

Inspired by the work [PA1], in this note, we prove that a complete set of pairwise orthogonal primitive idempotents of Yokonuma-Hecke algebras can be obtained by consecutive evaluations of a certain rational function.