The Harish-Chandra isomorphism for quantum GL2
Abstract
We construct an explicit Harish-Chandra isomorphism, from the quantum Hamiltonian reduction of the algebra Dq(GL2) of quantum differential operators on GL2, 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.
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