Semisimple Representations of Alternating Cyclotomic Hecke Algebras

Abstract

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 [23], [24].

Alternating quiver Hecke algebras

“…We discuss these algebras using a version of Clifford theory for associative algebras, and construct a homogeneous basis and a presentation by homogeneous generators and relations which are reminiscent of Khovanov and Lauda [14] and Rouquier's [22] theorems for quiver Hecke algebras. Cyclotomic quotients of these algebras are studied in [2] and [3]. This paper is organised as follows.…”