TY - JOUR AB - 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. AU - Koroteev, Peter AU - Pushkar, Petr AU - Smirnov, Andrey V. AU - Zeitlin, Anton M. ID - 9998 IS - 5 JF - Selecta Mathematica SN - 1022-1824 TI - Quantum K-theory of quiver varieties and many-body systems VL - 27 ER -