Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties
We prove a determinantal, Toda-type, presentation for the equivariant K theory of a partial flag variety Fl(₁, …, ₖ; ). The proof relies on pushing forward the Toda presentation obtained by Maeno, Naito, and Sagaki for the complete flag variety Fl(), via Kato's KT(pt)-algebra homomorphism from...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214184 |
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| Zitieren: | Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties. Kamyar Amini, Irit Huq-Kuruvilla, Leonardo C. Mihalcea, Daniel Orr and Weihong Xu. SIGMA 21 (2025), 098, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862572713936158720 |
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| author | Amini, Kamyar Huq-Kuruvilla, Irit Mihalcea, Leonardo C. Orr, Daniel Xu, Weihong |
| author_facet | Amini, Kamyar Huq-Kuruvilla, Irit Mihalcea, Leonardo C. Orr, Daniel Xu, Weihong |
| citation_txt | Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties. Kamyar Amini, Irit Huq-Kuruvilla, Leonardo C. Mihalcea, Daniel Orr and Weihong Xu. SIGMA 21 (2025), 098, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove a determinantal, Toda-type, presentation for the equivariant K theory of a partial flag variety Fl(₁, …, ₖ; ). The proof relies on pushing forward the Toda presentation obtained by Maeno, Naito, and Sagaki for the complete flag variety Fl(), via Kato's KT(pt)-algebra homomorphism from the quantum K ring of Fl() to that of Fl(₁, …, ₖ; ). Starting instead from the Whitney presentation for Fl(), we show that the same pushforward technique gives a recursive formula for polynomial representatives of quantum K Schubert classes in any partial flag variety which do not depend on quantum parameters. In an appendix, we include another proof of the Toda presentation for the equivariant quantum K ring of Fl(), following Anderson, Chen, and Tseng, which is based on the fact that the K-theoretic J-function is an eigenfunction of the finite difference Toda Hamiltonians.
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| first_indexed | 2026-03-21T11:47:01Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-214184 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:47:01Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
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| spelling | Amini, Kamyar Huq-Kuruvilla, Irit Mihalcea, Leonardo C. Orr, Daniel Xu, Weihong 2026-02-20T07:54:29Z 2025 Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties. Kamyar Amini, Irit Huq-Kuruvilla, Leonardo C. Mihalcea, Daniel Orr and Weihong Xu. SIGMA 21 (2025), 098, 26 pages 1815-0659 2020 Mathematics Subject Classification: 14M15; 14N35; 37K10; 05E05 arXiv:2504.07412 https://nasplib.isofts.kiev.ua/handle/123456789/214184 https://doi.org/10.3842/SIGMA.2025.098 We prove a determinantal, Toda-type, presentation for the equivariant K theory of a partial flag variety Fl(₁, …, ₖ; ). The proof relies on pushing forward the Toda presentation obtained by Maeno, Naito, and Sagaki for the complete flag variety Fl(), via Kato's KT(pt)-algebra homomorphism from the quantum K ring of Fl() to that of Fl(₁, …, ₖ; ). Starting instead from the Whitney presentation for Fl(), we show that the same pushforward technique gives a recursive formula for polynomial representatives of quantum K Schubert classes in any partial flag variety which do not depend on quantum parameters. In an appendix, we include another proof of the Toda presentation for the equivariant quantum K ring of Fl(), following Anderson, Chen, and Tseng, which is based on the fact that the K-theoretic J-function is an eigenfunction of the finite difference Toda Hamiltonians. The authors thank Dave Anderson, Linda Chen, Takeshi Ikeda, Shinsuke Iwao, Peter Koroteev, Takafumi Kouno, Satoshi Naito, Daisuke Sagaki, Mark Shimozono, and Kohei Yamaguchi for useful discussions and sharing insights related to this work. L.M. was partially supported by NSF grant DMS-2152294, and gratefully acknowledges the support of Charles Simonyi Endowment, which provided funding for the membership at the Institute of Advanced Study during the 2024-25 Special Year in ‘Algebraic and Geometric Combinatorics’. D.O. gratefully acknowledges support from the Simons Foundation. Finally, we are grateful to two anonymous referees for their valuable suggestions, which helped us improve the exposition of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties Article published earlier |
| spellingShingle | Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties Amini, Kamyar Huq-Kuruvilla, Irit Mihalcea, Leonardo C. Orr, Daniel Xu, Weihong |
| title | Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties |
| title_full | Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties |
| title_fullStr | Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties |
| title_full_unstemmed | Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties |
| title_short | Toda-Type Presentations for the Quantum K Theory of Partial Flag Varieties |
| title_sort | toda-type presentations for the quantum k theory of partial flag varieties |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214184 |
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