  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.
