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qKZ/tRS Duality via Quantum K-Theoretic Counts (1802.04463v4)
Published 13 Feb 2018 in math.AG, hep-th, math-ph, math.MP, math.QA, and math.RT
Abstract: 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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