Quantum difference equations for quiver varieties

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 identif...

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Main Author: Smirnov, Andrey
Language:English
Published: 2016
Subjects:
Quantum theory > Mathematics
K-theory
Difference equations
Weyl groups
Mathematics
Online Access:https://doi.org/10.7916/D8RN37T6
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spelling ndltd-columbia.edu-oai-academiccommons.columbia.edu-10.7916-D8RN37T62019-05-09T15:15:05ZQuantum difference equations for quiver varietiesSmirnov, Andrey2016ThesesQuantum theory--MathematicsK-theoryDifference equationsWeyl groupsMathematicsFor 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.Englishhttps://doi.org/10.7916/D8RN37T6
collection NDLTD
language English
sources NDLTD
topic Quantum theory--Mathematics
K-theory
Difference equations
Weyl groups
Mathematics
spellingShingle Quantum theory--Mathematics
K-theory
Difference equations
Weyl groups
Mathematics
Smirnov, Andrey
Quantum difference equations for quiver varieties
description 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.
author Smirnov, Andrey
author_facet Smirnov, Andrey
author_sort Smirnov, Andrey
title Quantum difference equations for quiver varieties
title_short Quantum difference equations for quiver varieties
title_full Quantum difference equations for quiver varieties
title_fullStr Quantum difference equations for quiver varieties
title_full_unstemmed Quantum difference equations for quiver varieties
title_sort quantum difference equations for quiver varieties
publishDate 2016
url https://doi.org/10.7916/D8RN37T6
work_keys_str_mv AT smirnovandrey quantumdifferenceequationsforquivervarieties
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