qKZ/tRS Duality via Quantum K-Theoretic Counts

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.

27 pages, 2 figures, to appear in Math. Res. Lett

References in corpus (5)

• Defects and Quantum Seiberg-Witten Geometry
• Lectures on Nakajima's Quiver Varieties
• Rationality of capped descendent vertex in $K$-theory
• On the quantum K-ring of the flag manifold
• On q-deformed gl(l+1)-Whittaker function

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• Branes and DAHA Representations
• Quasimaps to zero-dimensional $A_{\infty }$-quiver varieties
• Quantum K-theory and Integrability