Irreducible Specht modules for Iwahori-Hecke algebras of type B

TL;DR

This paper classifies irreducible Specht modules for Iwahori-Hecke algebras of type B, providing complete solutions for generic parameters and reducing the problem to type A when q=-1.

Contribution

It offers a complete classification of irreducible Specht modules for type B Iwahori-Hecke algebras, extending understanding in representation theory.

Findings

Complete classification for q not a root of unity

Reduction to type A when q=-1

Clarifies structure of Specht modules in type B

Abstract

We consider the problem of classifying irreducible Specht modules for the Iwahori-Hecke algebra of type B with parameters Q,q. We solve this problem completely in the case where q is not a root of unity, and in the case q=-1 we reduce the problem to the corresponding problem in type A.