Quantum Harish-Chandra isomorphism for the double affine Hecke algebra of $G{L}_n$

Abstract

We prove that for generic parameters, the quantum radial parts map of Varagnolo and Vasserot gives an isomorphism between the spherical double affine Hecke algebra of $G{L}_n$ and a quantized multiplicative quiver variety, as defined by Jordan.

v4, 41 pages. Final version. Incorporated referee's suggestions. Dedicated to Tom Nevins

References in corpus (4)

• Integrating quantum groups over surfaces
• The Harish-Chandra isomorphism for quantum GL_2
• Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras
• The rectangular representation of the double affine Hecke algebra via elliptic Schur-Weyl duality