Journal of Noncommutative Geometry


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Volume 12, Issue 3, 2018, pp. 1161–1197
DOI: 10.4171/JNCG/300

Published online: 2018-10-30

The Harish-Chandra isomorphism for quantum $GL_2$

Martina Balagovic[1] and David Jordan[2]

(1) University of Newcastle, UK
(2) University of Edinburgh, UK

We construct an explicit Harish-Chandra isomorphism, from the quantum Hamiltonian reduction of the algebra $\mathcal D_q(GL_2)$ 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 $q \in \mathbb C^{\times}$ and $t \neq ± i$, such that $q$ is not a non-trivial root of unity.

Keywords: Double affine Hecke algebra, quantum differential operators, factorization homology

Balagovic Martina, Jordan David: The Harish-Chandra isomorphism for quantum $GL_2$. J. Noncommut. Geom. 12 (2018), 1161-1197. doi: 10.4171/JNCG/300