Orthogonalization and polarization of Yangians
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914154964582400 |
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| author | Bock, Wolfgang Futorny, Vyacheslav Neklyudov, Mikhail Zhang, Jian |
| author_facet | Bock, Wolfgang Futorny, Vyacheslav Neklyudov, Mikhail Zhang, Jian |
| contents | For every family of orthogonal polynomials, we define a new realization of the Yangian of ${\mathfrak{gl}}_n$. Except in the case of Dickson polynomials, the new realizations do not satisfy the RTT relation. We obtain an analogue of the Christoffel-Darboux formula. Similar construction can be made for any family of functions satisfying certain recurrence relations, for example, $q$-Pochhhammer symbols and Bessel functions. Furthermore, using an analogue of the Jordan-Schwinger map, we define the ternary Yangian for a Lie algebra as a flat deformation of the current algebra of certain ternary extension of the given Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00259 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orthogonalization and polarization of Yangians Bock, Wolfgang Futorny, Vyacheslav Neklyudov, Mikhail Zhang, Jian Classical Analysis and ODEs Mathematical Physics Quantum Algebra Representation Theory For every family of orthogonal polynomials, we define a new realization of the Yangian of ${\mathfrak{gl}}_n$. Except in the case of Dickson polynomials, the new realizations do not satisfy the RTT relation. We obtain an analogue of the Christoffel-Darboux formula. Similar construction can be made for any family of functions satisfying certain recurrence relations, for example, $q$-Pochhhammer symbols and Bessel functions. Furthermore, using an analogue of the Jordan-Schwinger map, we define the ternary Yangian for a Lie algebra as a flat deformation of the current algebra of certain ternary extension of the given Lie algebra. |
| title | Orthogonalization and polarization of Yangians |
| topic | Classical Analysis and ODEs Mathematical Physics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2504.00259 |