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Quantum symmetric pairs and representations of double affine Hecke algebras of type \({C^\vee C_n}\)

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Abstract

We build representations of the affine and double affine braid groups and Hecke algebras of type \({C^\vee C_n}\) based upon the theory of quantum symmetric pairs (U, B). In the case \({{\bf U}=\mathcal{U}_{\rm q}(\mathfrak{gl}_N)}\), our constructions provide a quantization of the representations constructed by Etingof, Freund, and Ma in [15], and also a type \({C^\vee C_n}\) generalization of the results in [19].

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    David Jordan & Xiaoguang Ma

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  1. David Jordan
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  2. Xiaoguang Ma
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Correspondence to David Jordan.

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Jordan, D., Ma, X. Quantum symmetric pairs and representations of double affine Hecke algebras of type \({C^\vee C_n}\) . Sel. Math. New Ser. 17, 139–181 (2011). https://doi.org/10.1007/s00029-010-0037-8

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