Quantum difference equation for Nakajima varieties

A. Okounkov, A. Smirnov

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    1 Citation (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)1203-1299
    Number of pages97
    JournalInventiones Mathematicae
    Volume229
    Issue number3
    DOIs
    Publication statusPublished - Sep 2022

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