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The Harish-Chandra isomorphism for quantum GL_2 (1603.09218v1)
Published 30 Mar 2016 in math.RT and math.QA
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.