Characters of Ariki–Koike algebras

Abstract

In this paper, we prove the Regev formula for the characters of the Ariki–Koike algebras by applying the Schur–Sergeev reciprocity between quantum superalgebras and Ariki–Koike algebras. As a corollary, we derive the Regev formula for the characters of the complex reflection group of type $G(m,1,n)$, generalizing the Regev formula for the symmetric groups due to A. Regev (2013) [19].