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arXiv · 2312.06214

Duplex Hecke Algebras of type B

Yu Xie·An Zhang·Bin Shu
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Abstract

As a sequel to [14], in this article we first introduce a so-called duplex Hecke algebras of type B which is a Q(q)-algebra associated with the Weyl group W (B) of type B, and symmetric groups S_l for l = 0, 1, . . . ,m, satisfying some Hecke relations. This notion originates from the degenerate duplex Hecke algebra arising from the course of study of a kind of Schur-Weyl duality of Levi-type, extending the duplex Hecke algebra of type A arising from the related q-Schur-Weyl duality of Levi-type. A duplex Hecke algebra of type B admits natural representations on certain tensor spaces. We then establish a Levi-type q-Schur-Weyl duality of type B, which reveals the double centralizer property between such duplex Hecke algebras and {\i}quantum groups studied by Bao-Wang in [1].

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BibTeXRIS

Yu Xie, An Zhang, Bin Shu. 2023-12-11. Duplex Hecke Algebras of type B. https://arxiv.org/abs/2312.06214

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