Quantum difference equation for Nakajima varieties

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) circle times 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.

Automated summary

We construct an analog of quantum dynamical Weyl group in the equivariant K-theory of arbitrary Nakajima quiver variety X. The fundamental groupoid of a periodic locally finite hyperplane arrangement in Pic(X) circle times C serves as the correct generalization of the Weyl group in this context. The lattice part of this groupoid is identified with the operators of quantum difference equation for X. Examples are provided to illustrate the cases of quivers of finite and affine type.