The quantum Hikita conjecture via quasimaps

Hunter Dinkins, Ivan Karpov, Vasily Krylov

arXiv:2608.16746v1 Primary: math.AG Secondary: math.QA, math.RT

Abstract

We propose a refinement of the quantum Hikita conjecture of Kamnitzer, McBreen, and Proudfoot that bridges the representation theory of Coulomb branches with the enumerative geometry of Higgs branches. We also introduce a general framework for proving it, which we carry out for ADE quiver gauge theories with minuscule framings and for the gauge theory corresponding to the Jordan quiver. As an application, we use the resulting quantum Hikita isomorphisms to give a geometric description of graded traces on quantized Coulomb branches.

Disclosure

“by the Simons Foundation Award 888988 as part of the Simons Collaboration on Global Categorical Symmetries. V. Krylov apologizes for making an incorrect claim in a couple of talks he gave on this work; see footnote 3 below. We used ChatGPT 5.6 Sol (High and Pro versions) to assist with editing the manuscript, providing examples, references, and proofreading. 2 Hikita Conjectures, Graded Traces, and Quasimaps 2.1 Quiver gauge t”
PDF page 13

Classification: Suggesting mathematical examples or conjectures
Multiplier: 6
Verified: 2026-08-23T05:20:10.040023Z

Structural counts

Pages 107 pdf

Theorems 12 source

Lemmas 20 source

Propositions 33 source

Corollaries 6 source

Definitions 21 source

Displayed equations 452 source

Bibliography entries 131 source

Appendix pages 103 estimated

Count notes

Source counts use the expanded primary TeX file Hikita_arXiv-3.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.