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 Mitsuhashi (J. Alg. 240 535–558 2001, J. Alg. 264 231–250 2003).