Quantum K-theory of quiver varieties and many-body systems
Peter Koroteev, Petr P. Pushkar, Andrey V. Smirnov, Anton M. Zeitlin
Abstract
Abstract We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.
Topics & Concepts
QuiverEquivariant mapFlag (linear algebra)QuantumType (biology)Limit (mathematics)MathematicsPure mathematicsPhysicsChain (unit)Spin (aerodynamics)Quantum systemAlgebra over a fieldTheoretical physicsScheme (mathematics)TrigonometryQuantum groupVariety (cybernetics)Quantum field theoryTrigonometric functionsQuantum mechanicsAlgebraic structures and combinatorial modelsAdvanced Combinatorial MathematicsAlgebraic Geometry and Number Theory