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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212266 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Skew Symplectic and Orthogonal Schur Functions. Naihuan Jing, Zhijun Li and Danxia Wang. SIGMA 20 (2024), 041, 23 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |