# Quasimap counts and Bethe eigenfunctions

## TL;DR

This paper establishes a connection between quasimap counts, Bethe eigenfunctions, and quantum K-theory of Nakajima varieties, providing explicit formulas and solutions for related quantum equations.

## Contribution

It introduces explicit formulas linking descendent and relative insertions in quantum K-theory, and offers integral solutions for quantum equations associated with quivers.

## Key findings

- Explicit formulas for off-shell Bethe eigenfunctions
- Solutions to quantum Knizhnik-Zamolodchikov equations
- Connections between quasimap counts and quantum loop algebras

## Abstract

We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties. This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik-Zamolodchikov and dynamical q-difference equations.