Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras

TL;DR

This paper establishes isomorphisms between quantized Coulomb branches of Jordan quiver gauge theories and certain Cherednik algebras, revealing their algebraic structure and deformation properties.

Contribution

It proves the isomorphism of quantized Coulomb branches with spherical Cherednik algebras and describes their deformation relation to Yangians.

Findings

Quantized Coulomb branch is isomorphic to spherical graded Cherednik algebra in unframed case.

Quantized Coulomb branch is isomorphic to spherical cyclotomic rational Cherednik algebra in framed case.

Quantized Coulomb branch deforms a subquotient of the Yangian of affine gl(1).

Abstract

We study quantized Coulomb branches of quiver gauge theories of Jordan type. We prove that the quantized Coulomb branch is isomorphic to the spherical graded Cherednik algebra in the unframed case, and is isomorphic to the spherical cyclotomic rational Cherednik algebra in the framed case. We also prove that the quantized Coulomb branch is a deformation of a subquotient of the Yangian of the affine $\mathfrak{gl}(1)$.