Semisimple representations of alternating cyclotomic Hecke algebras

TL;DR

This paper introduces alternating cyclotomic Hecke algebras as subalgebras of cyclotomic Hecke algebras, computes their rank, and constructs all irreducible representations in the semisimple case, extending previous results.

Contribution

It defines higher-level alternating cyclotomic Hecke algebras and provides a complete classification of their irreducible representations in the semisimple setting.

Findings

Computed the rank of the algebras

Constructed all irreducible representations in the semisimple case

Generalized Mitsuhashi's results

Abstract

We define alternating cyclotomic Hecke algebras in higher levels as subalgebras of cyclotomic Hecke algebras under an analogue of Goldman's hash involution. We compute the rank of these algebras and construct a full set of irreducible representations in the semisimple case, generalising Mitsuhashi's results.