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.
Highlights
1.1 Some prehistory and earlier resultsThe seminal papers of Nekrasov and Shatashvili [40,41] paved the road for close interactions between quantum geometry of certain class of algebraic varieties and quantum integrable systems
Signs of such a fruitful collaboration between quantum cohomology/quantum K-theory and integrability were noted in mathematics literature in the works of Givental et al [20,23]
The generating function for such quantum tautological bundles is known in the theory of integrable systems as Baxter Q-operator which contains information about the spectrum of genuine physical Hamiltonians
Summary
The seminal papers of Nekrasov and Shatashvili [40,41] paved the road for close interactions between quantum geometry of certain class of algebraic varieties and quantum integrable systems. Signs of such a fruitful collaboration between quantum cohomology/quantum K-theory and integrability were noted in mathematics literature in the works of Givental et al [20,23]. Using a different method than in standard Gromov–Witten-inspired approach to quantum products, the quantum K-theory ring was defined, as well as the generators using the theory of quasimaps to GIT quotients [13,42].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have