qKZ/tRS duality via quantum $K$-theoretic counts
Peter Koroteev, Anton M. Zeitlin
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.
Topics & Concepts
MathematicsIntegrable systemQuantumTrigonometryEigenfunctionVertex (graph theory)Duality (order theory)Pure mathematicsTrigonometric functionsMathematical physicsCombinatoricsMathematical analysisQuantum mechanicsEigenvalues and eigenvectorsGraphPhysicsGeometryAlgebraic structures and combinatorial modelsNonlinear Waves and SolitonsAdvanced Topics in Algebra