Deformation Quantization with Separation of Variables of ₂‚₄(ℂ)
We construct a deformation quantization with separation of variables of the Grassmannian ₂‚₄(ℂ). A star product on ₂‚₄(ℂ) can be explicitly determined as the solution of the recurrence relations for ₂‚₄(ℂ) given by Hara and one of the authors (A. Sako). To provide a solution to the recurrence relati...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214175 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Deformation Quantization with Separation of Variables of ₂‚₄(ℂ). Taika Okuda and Akifumi Sako. SIGMA 21 (2025), 061, 32 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862679405516554240 |
|---|---|
| author | Okuda, Taika Sako, Akifumi |
| author_facet | Okuda, Taika Sako, Akifumi |
| citation_txt | Deformation Quantization with Separation of Variables of ₂‚₄(ℂ). Taika Okuda and Akifumi Sako. SIGMA 21 (2025), 061, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct a deformation quantization with separation of variables of the Grassmannian ₂‚₄(ℂ). A star product on ₂‚₄(ℂ) can be explicitly determined as the solution of the recurrence relations for ₂‚₄(ℂ) given by Hara and one of the authors (A. Sako). To provide a solution to the recurrence relations, it is necessary to solve a system of linear equations in each order. However, to give a concrete expression of the general term is not simple because the variables increase with the order of differentiation of the star product. For this reason, there has been no formula to express the general term of the recurrence relations. In this paper, we overcome this problem by transforming the recurrence relations into simpler ones. We solve the recurrence relations using creation and annihilation operators on a Fock space. From this solution, we obtain an explicit formula of a star product with separation of variables on ₂‚₄(ℂ).
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| first_indexed | 2026-03-16T21:08:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214175 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T21:08:32Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Okuda, Taika Sako, Akifumi 2026-02-19T16:04:53Z 2025 Deformation Quantization with Separation of Variables of ₂‚₄(ℂ). Taika Okuda and Akifumi Sako. SIGMA 21 (2025), 061, 32 pages 1815-0659 2020 Mathematics Subject Classification: 14M15; 32Q15; 46L87; 53D55 arXiv:2401.00500 https://nasplib.isofts.kiev.ua/handle/123456789/214175 https://doi.org/10.3842/SIGMA.2025.061 We construct a deformation quantization with separation of variables of the Grassmannian ₂‚₄(ℂ). A star product on ₂‚₄(ℂ) can be explicitly determined as the solution of the recurrence relations for ₂‚₄(ℂ) given by Hara and one of the authors (A. Sako). To provide a solution to the recurrence relations, it is necessary to solve a system of linear equations in each order. However, to give a concrete expression of the general term is not simple because the variables increase with the order of differentiation of the star product. For this reason, there has been no formula to express the general term of the recurrence relations. In this paper, we overcome this problem by transforming the recurrence relations into simpler ones. We solve the recurrence relations using creation and annihilation operators on a Fock space. From this solution, we obtain an explicit formula of a star product with separation of variables on ₂‚₄(ℂ). A.S. was supported by JSPS KAKENHI Grant Number 21K03258. The authors are grateful to Masashi Hamanaka, Shota Hamanaka, Yasushi Homma, Noriaki Ikeda, Taichiro Kugo, Thomas Raujouan, Hiroshi Tamaru, and Masashi Yasumo for useful advice and comments in “Mini-School on Differential Geometry and Integrable Systems”, “Poisson geometry and related topics23”, “The 4th International Conference on Surfaces, Analysis, and Numerics in Differential Geometry”, “Strings and Fields 2024”, and our private discussion at Nagoya University. The authors thank the Yukawa Institute for Theoretical Physics at Kyoto University. Discussions during the YITP workshop YITP-W-24-08 on “Strings and Fields 2024” were useful to complete this work. The authors sincerely appreciate the anonymous referees, whose thoughtful feedback on errors and typos contributed greatly to improving the quality of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Deformation Quantization with Separation of Variables of ₂‚₄(ℂ) Article published earlier |
| spellingShingle | Deformation Quantization with Separation of Variables of ₂‚₄(ℂ) Okuda, Taika Sako, Akifumi |
| title | Deformation Quantization with Separation of Variables of ₂‚₄(ℂ) |
| title_full | Deformation Quantization with Separation of Variables of ₂‚₄(ℂ) |
| title_fullStr | Deformation Quantization with Separation of Variables of ₂‚₄(ℂ) |
| title_full_unstemmed | Deformation Quantization with Separation of Variables of ₂‚₄(ℂ) |
| title_short | Deformation Quantization with Separation of Variables of ₂‚₄(ℂ) |
| title_sort | deformation quantization with separation of variables of ₂‚₄(ℂ) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214175 |
| work_keys_str_mv | AT okudataika deformationquantizationwithseparationofvariablesof24c AT sakoakifumi deformationquantizationwithseparationofvariablesof24c |