Characters of Ariki--Koike algebras

Deke Zhao

doi:10.1016/j.jalgebra.2025.07.023.

paper

Characters of Ariki--Koike algebras

arXiv:2410.15063 · doi:10.1016/j.jalgebra.2025.07.023.

Abstract

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).

13 pages, comments, suggestions and corrections are welcome