qKZ/tRS Duality via Quantum K-Theoretic Counts
Algebraic Geometry
2021-05-17 v4 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
Representation Theory
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.
Cite
@article{arxiv.1802.04463,
title = {qKZ/tRS Duality via Quantum K-Theoretic Counts},
author = {Peter Koroteev and Anton M. Zeitlin},
journal= {arXiv preprint arXiv:1802.04463},
year = {2021}
}
Comments
27 pages, 2 figures, to appear in Math. Res. Lett