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Mathematics > Quantum Algebra

arXiv:2210.01233 (math)
[Submitted on 3 Oct 2022 (v1), last revised 4 Jul 2023 (this version, v3)]

Title:Quantum supersymmetric pairs and $\imath$Schur duality of type AIII

Authors:Yaolong Shen
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Abstract:We construct quantum supersymmetric pairs $({\bold U},{\bold U}^\imath)$ of type AIII and elucidate their fundamental properties. An $\imath$Schur duality between the $\imath$quantum supergroup ${\bold U}^\imath$ and the Hecke algebra of type B acting on a tensor space is established, providing a super generalization of the $\imath$Schur duality of type AIII. Additionally, we construct a (quasi) $K$-matrix for arbitrary parameters, which facilitates the realization of the Hecke algebra action on the tensor space.
Comments: 43 pages; v2, references added; v3, major modifications to improve readablity
Subjects: Quantum Algebra (math.QA); Representation Theory (math.RT)
Cite as: arXiv:2210.01233 [math.QA]
  (or arXiv:2210.01233v3 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.2210.01233

Submission history

From: Yaolong Shen [view email]
[v1] Mon, 3 Oct 2022 21:09:33 UTC (39 KB)
[v2] Tue, 14 Mar 2023 23:48:54 UTC (39 KB)
[v3] Tue, 4 Jul 2023 07:03:14 UTC (40 KB)
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