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 GL_2 . The isomorphism holds for all deformation parameters q ∈ C× and t ≠ ± i , such that q is not a non-trivial root of unity.
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Balagović et al. (2018) studied this question.
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