Semisimple representations of alternating cyclotomic Hecke algebras

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.

arXiv comment18 pages; updated with new introduction and added motivation and application. Fixed minor typos