Quantum K-Theory of Grassmannians and Non-Abelian Localization

In the example of complex Grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of all such invariants using finite-difference operators, the ro...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2021
Автори: Givental, Alexander, Yan, Xiaohan
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2021
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211170
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Quantum K-Theory of Grassmannians and Non-Abelian Localization. Alexander Givental and Xiaohan Yan. SIGMA 17 (2021), 018, 24 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Givental, Alexander
Yan, Xiaohan
author_facet Givental, Alexander
Yan, Xiaohan
citation_txt Quantum K-Theory of Grassmannians and Non-Abelian Localization. Alexander Givental and Xiaohan Yan. SIGMA 17 (2021), 018, 24 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description In the example of complex Grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of all such invariants using finite-difference operators, the role of the -hypergeometric series arising in the context of quasimap compactifications of spaces of rational curves in such varieties, the theory of twisted GW-invariants, including level structures, as well as the Jackson-type integrals playing the role of equivariant K-theoretic mirrors.
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last_indexed 2026-03-15T11:48:05Z
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publisher Інститут математики НАН України
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spelling Givental, Alexander
Yan, Xiaohan
2025-12-25T13:21:10Z
2021
Quantum K-Theory of Grassmannians and Non-Abelian Localization. Alexander Givental and Xiaohan Yan. SIGMA 17 (2021), 018, 24 pages
1815-0659
2020 Mathematics Subject Classification: 14N35
arXiv:2008.08182
https://nasplib.isofts.kiev.ua/handle/123456789/211170
https://doi.org/10.3842/SIGMA.2021.018
In the example of complex Grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of all such invariants using finite-difference operators, the role of the -hypergeometric series arising in the context of quasimap compactifications of spaces of rational curves in such varieties, the theory of twisted GW-invariants, including level structures, as well as the Jackson-type integrals playing the role of equivariant K-theoretic mirrors.
This material is based upon work supported by the National Science Foundation under Grant DMS-1906326. We are thankful to P. Koroteev and A. Smirnov for their effort in educating us about their work on quantum K-theory of symplectic quiver varieties, and to H. Liu and Y. Wen for sharing and discussing their preprints.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Quantum K-Theory of Grassmannians and Non-Abelian Localization
Article
published earlier
spellingShingle Quantum K-Theory of Grassmannians and Non-Abelian Localization
Givental, Alexander
Yan, Xiaohan
title Quantum K-Theory of Grassmannians and Non-Abelian Localization
title_full Quantum K-Theory of Grassmannians and Non-Abelian Localization
title_fullStr Quantum K-Theory of Grassmannians and Non-Abelian Localization
title_full_unstemmed Quantum K-Theory of Grassmannians and Non-Abelian Localization
title_short Quantum K-Theory of Grassmannians and Non-Abelian Localization
title_sort quantum k-theory of grassmannians and non-abelian localization
url https://nasplib.isofts.kiev.ua/handle/123456789/211170
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AT yanxiaohan quantumktheoryofgrassmanniansandnonabelianlocalization