Forum of Mathematics, Sigma (Jan 2024)

Quantum wreath products and Schur–Weyl duality I

  • Chun-Ju Lai,
  • Daniel K. Nakano,
  • Ziqing Xiang

DOI
https://doi.org/10.1017/fms.2024.103
Journal volume & issue
Vol. 12

Abstract

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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.

Keywords