Isomorphisms between simple modules of degenerate cyclotomic Hecke algebras

TL;DR

This paper constructs explicit isomorphisms between simple modules of degenerate cyclotomic Hecke algebras using different cellular bases, and introduces a generalized Mullineux involution in the degenerate setting.

Contribution

It provides explicit module isomorphisms and a new generalized Mullineux involution for degenerate cyclotomic Hecke algebras, advancing understanding of their representation theory.

Findings

Explicit isomorphisms between simple modules via cellular bases

Introduction of a generalized Mullineux involution in the degenerate case

Enhanced understanding of module structures in degenerate cyclotomic Hecke algebras

Abstract

We give explicit isomorphisms between simple modules of degenerate cyclotomic Hecke algebras defined via various cellular bases. A special case gives a generalized Mullineux involution in the degenerate case.