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arXiv · 2606.03759

On Cellularity of Hecke Algebras for Wreath Products

Berta Hudak·Chun-Ju Lai
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Abstract

The (generalized) Hu algebra is a nontrivial quantization of the wreath product $\Sigma_m \wr \Sigma_d$ between symmetric groups, whose representation theory controls the Hecke algebra of the complex reflection group $G(d,d,md)$. In this paper, we construct a unified basis for this algebra and establish its cellular algebra structure in the case $d = 2$. As an application, our construction provides an elementary realization of the simple modules for the Hecke algebra of type $D_{2m}$ that are parameterized by bipartitions of size $(m,m)$.

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BibTeXRIS

Berta Hudak, Chun-Ju Lai. 2026-06-02. On Cellularity of Hecke Algebras for Wreath Products. https://arxiv.org/abs/2606.03759

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