Skew Symplectic and Orthogonal Schur Functions
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914803418660864 |
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| author | Jing, Naihuan Li, Zhijun Wang, Danxia |
| author_facet | Jing, Naihuan Li, Zhijun Wang, Danxia |
| contents | Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey 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 offers unified realizations for skew Schur functions of types A, C, and D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_05526 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Skew Symplectic and Orthogonal Schur Functions Jing, Naihuan Li, Zhijun Wang, Danxia Combinatorics Quantum Algebra Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey 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 offers unified realizations for skew Schur functions of types A, C, and D. |
| title | Skew Symplectic and Orthogonal Schur Functions |
| topic | Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2208.05526 |