TL;DR
This paper proves Regev's formulas for characters of Ariki--Koike algebras using Schur--Sergeev reciprocity, extending previous results to complex reflection groups of type G(m,1,n).
Contribution
It generalizes Regev's character formulas to Ariki--Koike algebras via quantum superalgebra methods.
Findings
Proved Regev formulae for Ariki--Koike algebra characters.
Extended formulas to complex reflection groups of type G(m,1,n).
Utilized Schur--Sergeev reciprocity in the proofs.
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 , which is a generalization of the formulas in (A. Regev, Israel J. Math. 195 (2013): 31--35).
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Algebraic structures and combinatorial models