Quantum difference equation for Nakajima varieties

• 成果类型: Article
• 署名作者: Okounkov, A.; Smirnov, A.
• 署名单位: Columbia University; HSE University (National Research University Higher School of Economics); University of North Carolina; University of North Carolina Chapel Hill; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01125-w
• 发表日期: 2022
• 页码: 1203-1299
• 关键词: donaldson-thomas theory; gromov-witten theory; quiver varieties; macdonald polynomials; hilbert scheme; K-THEORY; ALGEBRAS; degeneration; REPRESENTATIONS; QUANTIZATION

摘要

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) circle times 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.