Quantum difference equation for Nakajima varieties
Quantum difference equation for Nakajima varieties
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DOI：
10.1007/s00222-022-01125-w
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发表时间：
2016-02
影响因子：
3.1
通讯作者：
A. Okounkov;A. Smirnov
中科院分区：
文献类型：
--
作者：
A. Okounkov;A. Smirnov
对于任意的Nakajima箭图变体X，我们构造了量子动力学Weyl群在其等变K-理论中的模拟。这里Weyl群的正确推广是文[1]中某一周期局部有限超平面排列的基本群胚。我们用X的量子差分方程的算符来确定这个群的格子部分。文中给出了有限箭图和仿射箭图的例子。
For an arbitrary Nakajima quiver varietyX, 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. We identify the lattice part of this groupoid with the operators of quantum difference equation forX. The cases of quivers of finite and affine type are illustrated by explicit examples.