Minor identities for Sklyanin determinants
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866908288711393280 |
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| author | Jing, Naihuan Zhang, Jian |
| author_facet | Jing, Naihuan Zhang, Jian |
| contents | We explore the invariant theory of quantum symmetric spaces of orthogonal and symplectic types by employing R-matrix techniques. Our focus involves establishing connections among the quantum determinant, Sklyanin determinants associated with the orthogonal and symplectic cases, and the quantum Pfaffians over the symplectic quantum space. Drawing inspiration from twisted Yangians, we not only demonstrate but also extend the applicability of q-Jacobi identities, q-Cayley's complementary identities, q-Sylvester identities, and Muir's theorem to Sklyanin minors in both orthogonal and symplectic types, along with q-Pfaffian analogs in the symplectic scenario. Furthermore, we present expressions for Sklyanin determinants and quantum Pfaffians in terms of quasideterminants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04775 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Minor identities for Sklyanin determinants Jing, Naihuan Zhang, Jian Quantum Algebra Rings and Algebras Primary: 17B37, Secondary: 58A17, 15A75, 15B33, 15A15 We explore the invariant theory of quantum symmetric spaces of orthogonal and symplectic types by employing R-matrix techniques. Our focus involves establishing connections among the quantum determinant, Sklyanin determinants associated with the orthogonal and symplectic cases, and the quantum Pfaffians over the symplectic quantum space. Drawing inspiration from twisted Yangians, we not only demonstrate but also extend the applicability of q-Jacobi identities, q-Cayley's complementary identities, q-Sylvester identities, and Muir's theorem to Sklyanin minors in both orthogonal and symplectic types, along with q-Pfaffian analogs in the symplectic scenario. Furthermore, we present expressions for Sklyanin determinants and quantum Pfaffians in terms of quasideterminants. |
| title | Minor identities for Sklyanin determinants |
| topic | Quantum Algebra Rings and Algebras Primary: 17B37, Secondary: 58A17, 15A75, 15B33, 15A15 |
| url | https://arxiv.org/abs/2208.04775 |