Characters of Ariki--Koike algebras

In this paper, we prove the Regev formulae for the characters of the Ariki–Koike algebras by applying the Schur–Sergeev reciprocity between the quantum superalgebras and the Ariki–Koike algebras, which is a generalization of the formulas in (D. Zhao, Israel J. Math. 229 (2019): 67–83 ). As a corollary, we provide the Regev formulae for the characters of the complex reflection group of type $G(m,1,n)$, which is a generalization of the formulas in (A. Regev, Israel J. Math. 195 (2013): 31–35).