Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus
The self-dual spaces of polynomials are related to Bethe vectors in the Gaudin model associated to the Lie algebras of types B and C. In this paper, we give lower bounds for the number of real self-dual spaces in intersections of Schubert varieties related to osculating flags in the Grassmannian. Th...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209526 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus / K. Lu // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862540530756354048 |
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| author | Lu, K. |
| author_facet | Lu, K. |
| citation_txt | Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus / K. Lu // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The self-dual spaces of polynomials are related to Bethe vectors in the Gaudin model associated to the Lie algebras of types B and C. In this paper, we give lower bounds for the number of real self-dual spaces in intersections of Schubert varieties related to osculating flags in the Grassmannian. The higher Gaudin Hamiltonians are self-adjoint with respect to a nondegenerate indefinite Hermitian form. Our bound comes from the computation of the signature of this form.
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| first_indexed | 2025-12-03T09:54:13Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209526 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-03T09:54:13Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lu, K. 2025-11-24T10:40:49Z 2018 Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus / K. Lu // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14N99; 17B80; 82B23 arXiv: 1710.06534 https://nasplib.isofts.kiev.ua/handle/123456789/209526 https://doi.org/10.3842/SIGMA.2018.046 The self-dual spaces of polynomials are related to Bethe vectors in the Gaudin model associated to the Lie algebras of types B and C. In this paper, we give lower bounds for the number of real self-dual spaces in intersections of Schubert varieties related to osculating flags in the Grassmannian. The higher Gaudin Hamiltonians are self-adjoint with respect to a nondegenerate indefinite Hermitian form. Our bound comes from the computation of the signature of this form. The author thanks E. Mukhin and V. Tarasov for useful discussions. The author also thanks the referees for their comments and suggestions that substantially improved the first version of this paper. This work was partially supported by the Zhejiang Province Science Foundation, grant No. LY14A010018. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus Article published earlier |
| spellingShingle | Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus Lu, K. |
| title | Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus |
| title_full | Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus |
| title_fullStr | Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus |
| title_full_unstemmed | Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus |
| title_short | Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus |
| title_sort | lower bounds for numbers of real self-dual spaces in problems of schubert calculus |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209526 |
| work_keys_str_mv | AT luk lowerboundsfornumbersofrealselfdualspacesinproblemsofschubertcalculus |