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Quantum difference equations for quiver varieties

Smirnov, Andrey

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)⊗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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More About This Work

Academic Units
Mathematics
Thesis Advisors
Okounkov, Andrei
Degree
Ph.D., Columbia University
Published Here
April 14, 2016
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