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Working paper

Quantum difference equation for Nakajima varieties

arXiv:1602.09007v1. arXiv:1602.09007 . Mathematical Physics (math-ph), 2016. No. 29.
Okounkov A., Smirnov А.
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. 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.