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arXiv · 2511.19825

Quantum wreath products and Schur--Weyl duality II

Chun-Ju Lai·Daniel K. Nakano·Ziqing Xiang
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Abstract

In the first part of this series, the authors introduced the quantum wreath product, providing a unified framework that encompasses numerous results previously addressed only through case-by-case analysis. This paper shifts focus to the fundamental construction of modules over these products, termed wreath modules. Our approach utilizes parabolic induction on tensor products combined with a sophisticated labeling scheme based on multipartitions. While the underlying constructions are technically involved, they offer a transparent realization of several prominent module families. Specifically, these wreath modules recover and unify: Simple modules over the Ariki-Koike algebra; Specht and simple modules over the Hu algebra; (anti)spherical modules and Kashiwara-Miwa-Stern modules over the affine Hecke algebra and its pro-p Iwahori variants. Finally, we demonstrate that these wreath modules for the Hu algebra serve as a critical component in solving the Ginzburg-Guay-Opdam-Rouquier problem. This solution enables a concrete realization of Category O for the rational Cherednik algebra in Type D.

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Chun-Ju Lai, Daniel K. Nakano, Ziqing Xiang. 2026-05-26. Quantum wreath products and Schur--Weyl duality II. https://arxiv.org/abs/2511.19825

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