Quantum difference equation for Nakajima varieties

Abstract

For an arbitrary Nakajima quiver variety $X$, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in $Pic(X)\otimes \mathbb{C}$. We identify the lattice part of this groupoid with the operators of quantum difference equation for $X$. The cases of quivers of finite and affine type are illustrated by explicit examples.

105 pages, 3 figures

Cited by in corpus (2)

• Motivic Chern classes and K-theoretic stable envelopes
• qKZ/tRS Duality via Quantum K-Theoretic Counts