The Harish-Chandra isomorphism for quantum GL_2

Abstract

We construct an explicit Harish-Chandra isomorphism, from the quantum Hamiltonian reduction of the algebra D_q(GL_2) of quantum differential operators on GL_2, to the spherical double affine Hecke algebra associated to GL2. The isomorphism holds for all deformation parameters non-zero q, t, such that t does not equal to +/-i, and q is not a non-trivial root of unity. We also discuss its extension to the root of unity case.

References in corpus (3)

• Integrating quantum groups over surfaces
• Quantizations of multiplicative hypertoric varieties at a root of unity
• The Harish-Chandra isomorphism for quantum GL_2

Cited by in corpus (3)

• The Harish-Chandra isomorphism for quantum GL_2
• Kauffman Skein Algebras and Quantum Teichmüller Spaces via Factorisation Homology
• Quantum Harish-Chandra isomorphism for the double affine Hecke algebra of $G{L}_n$