Quantum wreath products and Schur–Weyl duality I

In this paper, the authors introduce a new notion called the quantum wreath product, which is the algebra $B \wr _Q \mathcal {H}(d)$ produced from a given algebra B, a positive integer d and a choice $Q=(R,S,\rho ,\sigma )$ of parameters. Important examples that arise from our construc...

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Bibliographic Details
Main Authors: Chun-Ju Lai, Daniel K. Nakano, Ziqing Xiang
Format: Article
Language:English
Published: Cambridge University Press 2024-01-01
Series:Forum of Mathematics, Sigma
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Online Access:https://www.cambridge.org/core/product/identifier/S2050509424001038/type/journal_article
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Summary:In this paper, the authors introduce a new notion called the quantum wreath product, which is the algebra $B \wr _Q \mathcal {H}(d)$ produced from a given algebra B, a positive integer d and a choice $Q=(R,S,\rho ,\sigma )$ of parameters. Important examples that arise from our construction include many variants of the Hecke algebras, such as the Ariki–Koike algebras, the affine Hecke algebras and their degenerate version, Wan–Wang’s wreath Hecke algebras, Rosso–Savage’s (affine) Frobenius Hecke algebras, Kleshchev–Muth’s affine zigzag algebras and the Hu algebra that quantizes the wreath product $\Sigma _m \wr \Sigma _2$ between symmetric groups.
ISSN:2050-5094