qKZ/tRS Duality via Quantum K-Theoretic Counts

TL;DR

This paper establishes a connection between quantum K-theoretic vertex functions of cotangent bundles of partial flag varieties and eigenfunctions of quantum tRS Hamiltonians, revealing new identities via qKZ equations.

Contribution

It demonstrates that normalized quantum K-theoretic vertex functions are eigenfunctions of quantum tRS Hamiltonians and derives new identities linking qKZ equations and tRS systems.

Findings

Vertex functions are eigenfunctions of quantum tRS Hamiltonians.

Derived a new identity relating qKZ equations and tRS integrable system.

Established a link between quantum K-theory and integrable models.

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.