The hook fusion procedure for Hecke algebras

TL;DR

This paper introduces a novel fusion procedure for Hecke algebras that uses principal hooks of Young diagrams to efficiently generate irreducible representations with fewer parameters.

Contribution

It presents a new expression for the q-analogue of Young symmetrizers based on Cherednik's fusion procedure focusing on principal hooks, reducing auxiliary parameters.

Findings

New expression for q-analogue of Young symmetrizers

Reduced number of auxiliary parameters in fusion process

Efficient generation of irreducible Hecke algebra representations

Abstract

We derive a new expression for the q-analogue of the Young symmetrizer which generate irreducible representations of the Hecke algebra. We obtain this new expression using Cherednik's fusion procedure. However, instead of splitting Young diagrams into their rows or columns, we consider their principal hooks. This minimises the number of auxiliary parameters needed in the fusion procedure.