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arXiv · 1602.09007

Quantum difference equation for Nakajima varieties

Andrei Okounkov·Andrey Smirnov
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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.

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Andrei Okounkov, Andrey Smirnov. 2016-02-29. Quantum difference equation for Nakajima varieties. https://arxiv.org/abs/1602.09007

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