Quantum difference equation for Nakajima varieties

Kavli Affiliate: Andrei Okounkov

| First 5 Authors: Andrei Okounkov, Andrey Smirnov, , ,

| Summary:

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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