Quantum D-modules, elliptic braid groups, and double affine Hecke algebras

Details Quantum D-modules, elliptic braid groups, and double affine Hecke algebras Quantum D-modules, elliptic braid groups, and double affine Hecke algebras

2008-05-19

arxiv.org/abs/0805.2766v2

Int. Math. Res. Not. (2009) 2081-2105

Mathematics

Quantum Algebra

Scientific paper

10.1093/imrp/rnp012

We build representations of the elliptic braid group from the data of a quantum D-module M over a ribbon Hopf algebra U. The construction is modelled on, and generalizes, similar constructions by Lyubashenko and Majid, and also certain geometric constructions of Calaque, Enriquez, and Etingof concerning trigonometric Cherednik algebras. In this context, the former construction is the special case where M is the basic representation, while the latter construction can be recovered as a quasi-classical limit of U=U_t(sl_N), as t limits 1. In the latter case, we produce representations of the double affine Hecke algebra of type A_{n-1}, for each n.

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