TL;DR
This paper extends classical theorems to the quantum setting for Iwahori-Hecke algebras using Schur-Weyl duality and skew character theory, providing new proofs and insights into their characters.
Contribution
It introduces a quantum generalization of Regev's theorems for Iwahori-Hecke algebras and offers alternative proofs via skew character theory.
Findings
Quantum generalization of Regev's theorems established
Schur-Weyl duality applied to quantum superalgebras
Alternative proof using skew character theory provided
Abstract
In this paper we prove a quantum generalization of Regev's theorems in (Israel. J. Math. 195 (2013), 31--35) by applying the Schur-Weyl duality between the quantum superalgebra and Iwahori-Hecke algebra. We also present an alternative proof of the quantized generalizations using the skew character theory of Iwahori-Hecke algebras.
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