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qKZ/tRS Duality via Quantum K-Theoretic Counts

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arxiv 1802.04463 v4 pith:VVWMWPAI submitted 2018-02-13 math.AG hep-thmath-phmath.MPmath.QAmath.RT

Peter Koroteev , Anton M. Zeitlin This is my paper · ORCID
classification math.AGhep-thmath-phmath.MPmath.QAmath.RT
keywords quantumfunctionsk-theoreticvertexbundlescotangentcountsderive
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We show that normalized quantum K-theoretic vertex functions for cotangent bundles of partial flag varieties are the eigenfunctions of quantum trigonometric Ruijsenaars-Schneider (tRS) Hamiltonians. Using recently observed relations between quantum Knizhnik-Zamolodchikov (qKZ) equations and tRS integrable system we derive a nontrivial identity for vertex functions with relative insertions.

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  1. Rationality of the K-theoretical capped vertex function for Nakajima quiver varieties

    math.AG 2024-11 conditional novelty 7.0 of 10

    For any Nakajima quiver variety with generic stability condition, the capped vertex function with descendents is a rational function of the Kähler variables.

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