Skew Symplectic and Orthogonal Schur Functions
Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show that they are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by Koike and Terada and satisfy the general branching rules. Furt...
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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/123456789/212266 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Skew Symplectic and Orthogonal Schur Functions. Naihuan Jing, Zhijun Li and Danxia Wang. SIGMA 20 (2024), 041, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862750823882162176 |
|---|---|
| author | Jing, Naihuan Li, Zhijun Wang, Danxia |
| author_facet | Jing, Naihuan Li, Zhijun Wang, Danxia |
| citation_txt | Skew Symplectic and Orthogonal Schur Functions. Naihuan Jing, Zhijun Li and Danxia Wang. SIGMA 20 (2024), 041, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show that they are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by Koike and Terada and satisfy the general branching rules. Furthermore, we derive the Jacobi-Trudi identities and Gelfand-Tsetlin patterns for these symmetric functions. Additionally, the vertex operator method yields their Cauchy-type identities. This demonstrates that vertex operator representations serve not only as a tool for studying symmetric functions but also offer unified realizations for skew Schur functions of types A, C, and D.
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| first_indexed | 2026-03-21T18:14:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212266 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:14:36Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Jing, Naihuan Li, Zhijun Wang, Danxia 2026-02-03T07:58:09Z 2024 Skew Symplectic and Orthogonal Schur Functions. Naihuan Jing, Zhijun Li and Danxia Wang. SIGMA 20 (2024), 041, 23 pages 1815-0659 2020 Mathematics Subject Classification: 05E05; 17B37 arXiv:2208.05526 https://nasplib.isofts.kiev.ua/handle/123456789/212266 https://doi.org/10.3842/SIGMA.2024.041 Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show that they are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by Koike and Terada and satisfy the general branching rules. Furthermore, we derive the Jacobi-Trudi identities and Gelfand-Tsetlin patterns for these symmetric functions. Additionally, the vertex operator method yields their Cauchy-type identities. This demonstrates that vertex operator representations serve not only as a tool for studying symmetric functions but also offer unified realizations for skew Schur functions of types A, C, and D. We extend our heartfelt appreciation to the anonymous referees for their invaluable constructive feedback and suggestions, which have enhanced the quality of the paper. The research is supported by the Simons Foundation (grant no. MP-TSM-00002518), NSFC (grant nos. 12171303, 12101231, 12301033), and NSF of Huzhou (grant no. 2022YZ47). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Skew Symplectic and Orthogonal Schur Functions Article published earlier |
| spellingShingle | Skew Symplectic and Orthogonal Schur Functions Jing, Naihuan Li, Zhijun Wang, Danxia |
| title | Skew Symplectic and Orthogonal Schur Functions |
| title_full | Skew Symplectic and Orthogonal Schur Functions |
| title_fullStr | Skew Symplectic and Orthogonal Schur Functions |
| title_full_unstemmed | Skew Symplectic and Orthogonal Schur Functions |
| title_short | Skew Symplectic and Orthogonal Schur Functions |
| title_sort | skew symplectic and orthogonal schur functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212266 |
| work_keys_str_mv | AT jingnaihuan skewsymplecticandorthogonalschurfunctions AT lizhijun skewsymplecticandorthogonalschurfunctions AT wangdanxia skewsymplecticandorthogonalschurfunctions |