Quantum K-theory of quiver varieties and many-body systems

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.

Automated summary

In this paper, the quantum equivariant K-theory of Nakajima quiver varieties is defined and the details of type A are discussed, including its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Furthermore, a limit is studied which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.