Quantum symmetric pairs and representations of double affine Hecke algebras of type $C^{\vee }{C}_n$

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 $U=U_q(g{l}_N)$, our constructions provide a quantization of the representations constructed by Etingof, Freund and Ma in arXiv:0801.1530, and also a type $BC$ generalization of the results in arXiv:0805.2766.

Final version, to appear in Selecta Mathematica

References in corpus (2)

• Method of quantum characters in equivariant quantization
• Quantum D-modules, elliptic braid groups, and double affine Hecke algebras

Cited by in corpus (1)

• Suzuki functor at the critical level