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Quantum difference equations for quiver 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)⊗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.

Identiferoai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/D8RN37T6
Date January 2016
CreatorsSmirnov, Andrey
Source SetsColumbia University
LanguageEnglish
Detected LanguageEnglish
TypeTheses

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