The Harish-Chandra isomorphism for quantum GL(2)

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 is an element of C-x and t not equal +/- i, such that q is not a non-trival root of unity.