K-theoretic Hikita conjecture for quiver gauge theories

Abstract

We study variants of Hikita conjecture for Nakajima quiver varieties and corresponding Coulomb branches. First, we derive the equivariant version of the conjecture from the non-equivariant one for a set of gauge theories. Second, we suggest a variant of the conjecture, with K-theoretic Coulomb branches involved. We show that this version follows from the usual (homological) one for a set of theories. We apply this result to prove the conjecture in finite ADE types. In the course of the proof, we show that appropriate completions of K-theoretic and homological (quantized) Coulomb branches are isomorphic.

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