Quantum Harish-Chandra isomorphism for the double affine Hecke algebra of $GL_n$

TL;DR

This paper establishes an isomorphism between the spherical double affine Hecke algebra of $GL_n$ and a quantized multiplicative quiver variety for generic parameters, extending the quantum Harish-Chandra isomorphism to this setting.

Contribution

It proves a new isomorphism linking the spherical double affine Hecke algebra of $GL_n$ with a quantized multiplicative quiver variety, generalizing previous results.

Findings

Isomorphism holds for generic parameters.

Connects double affine Hecke algebra with quiver varieties.

Extends quantum Harish-Chandra theory.

Abstract

We prove that for generic parameters, the quantum radial parts map of Varagnolo and Vasserot gives an isomorphism between the spherical double affine Hecke algebra of $GL_n$ and a quantized multiplicative quiver variety, as defined by Jordan.