The HarishChandra isomorphism for quantum GL_2
Abstract
We construct an explicit HarishChandra 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 nonzero q, t, such that t does not equal to +/i, and q is not a nontrivial root of unity. We also discuss its extension to the root of unity case.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.09218
 Bibcode:
 2016arXiv160309218B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra;
 81R50;
 58B32;
 17B37
 EPrint:
 Published in Journal of Noncommutative Geometry 2016