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arXiv · 2509.06226

K-theoretic Hikita conjecture for quiver gauge theories

Ilya Dumanski·Vasily Krylov
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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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BibTeXRIS

Ilya Dumanski, Vasily Krylov. 2025-09-07. K-theoretic Hikita conjecture for quiver gauge theories. https://arxiv.org/abs/2509.06226

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