Geometry of Integrable Systems Related to the Restricted Grassmannian
A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture is presented.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212788 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Geometry of Integrable Systems Related to the Restricted Grassmannian. Tomasz Goliński and Alice Barbora Tumpach. SIGMA 20 (2024), 104, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862607448652644352 |
|---|---|
| author | Goliński, Tomasz Tumpach, Alice Barbora |
| author_facet | Goliński, Tomasz Tumpach, Alice Barbora |
| citation_txt | Geometry of Integrable Systems Related to the Restricted Grassmannian. Tomasz Goliński and Alice Barbora Tumpach. SIGMA 20 (2024), 104, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture is presented.
|
| first_indexed | 2026-03-21T11:56:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212788 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:56:10Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Goliński, Tomasz Tumpach, Alice Barbora 2026-02-11T10:40:05Z 2024 Geometry of Integrable Systems Related to the Restricted Grassmannian. Tomasz Goliński and Alice Barbora Tumpach. SIGMA 20 (2024), 104, 18 pages 1815-0659 2020 Mathematics Subject Classification: 70H06; 53D20; 53D17; 46T05; 47B10 arXiv:2407.21605 https://nasplib.isofts.kiev.ua/handle/123456789/212788 https://doi.org/10.3842/SIGMA.2024.104 A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture is presented. This research of the authors was partially supported by a joint National Science Centre, Poland (number 2020/01/Y/ST1/00123) and Fonds zur Förderung der wissenschaftlichen Forschung, Austria (number I 5015-N) grant “Banach Poisson–Lie groups and integrable systems”. The authors would like to thank the Erwin Schrödinger Institute for its hospitality during the thematic programme “Geometry beyond Riemann: Curvature and Rigidity” in September 2023. The stimulating atmosphere of the Workshop on Geometric Methods in Physics in Bialowieza, Poland, is also acknowledged, where both authors could meet to work on this paper. The authors are grateful to the referees for their remarks and suggestions, which improved the presentation of the results. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geometry of Integrable Systems Related to the Restricted Grassmannian Article published earlier |
| spellingShingle | Geometry of Integrable Systems Related to the Restricted Grassmannian Goliński, Tomasz Tumpach, Alice Barbora |
| title | Geometry of Integrable Systems Related to the Restricted Grassmannian |
| title_full | Geometry of Integrable Systems Related to the Restricted Grassmannian |
| title_fullStr | Geometry of Integrable Systems Related to the Restricted Grassmannian |
| title_full_unstemmed | Geometry of Integrable Systems Related to the Restricted Grassmannian |
| title_short | Geometry of Integrable Systems Related to the Restricted Grassmannian |
| title_sort | geometry of integrable systems related to the restricted grassmannian |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212788 |
| work_keys_str_mv | AT golinskitomasz geometryofintegrablesystemsrelatedtotherestrictedgrassmannian AT tumpachalicebarbora geometryofintegrablesystemsrelatedtotherestrictedgrassmannian |