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 |
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| Дата: | 2021 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862646848788889600 |
|---|---|
| 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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| first_indexed | 2026-03-15T11:48:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211170 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T11:48:05Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT giventalalexander quantumktheoryofgrassmanniansandnonabelianlocalization AT yanxiaohan quantumktheoryofgrassmanniansandnonabelianlocalization |