# Quantum K-theory of Quiver Varieties and Many-Body Systems

## TL;DR

This paper develops the quantum equivariant K-theory for Nakajima quiver varieties, linking it to integrable systems like XXZ spin chains and Ruijsenaars-Schneider models, and explores its relation to quantum geometry of flag varieties and Toda lattice.

## Contribution

It introduces a new framework for quantum K-theory of quiver varieties and connects it to integrable systems and quantum geometry, extending previous results in the field.

## Key findings

- Defined quantum equivariant K-theory for Nakajima quiver varieties
- Established connections with quantum XXZ spin chains and Ruijsenaars-Schneider models
- Linked quantum geometry of flag varieties with Toda lattice through a limiting process

## 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.