Representation Theory of the Twisted Yangians in Complex Rank
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909606388695040 |
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| author | Kannan, Arun S. Kanungo, Shihan |
| author_facet | Kannan, Arun S. Kanungo, Shihan |
| contents | In 2016, Etingof defined the notion of a Yangian in a symmetric tensor category and posed the problem to study them in the context of Deligne categories. This problem was studied by Kalinov in 2020 for the Yangian $Y(\mathfrak{gl}_t)$ of the general linear Lie algebra $\mathfrak{gl}_t$ in complex rank using the techniques of ultraproducts. In particular, Kalinov classified the simple finite-length modules over $Y(\mathfrak{gl}_t)$. In this paper, we define the notion of a twisted Yangian in Deligne's categories, and we extend these techniques to classify finite-length simple modules over the twisted Yangians $Y(\mathfrak{o}_t)$ and $Y(\mathfrak{sp}_t)$ of the orthogonal and symplectic Lie algebras $\mathfrak{o}_t,\mathfrak{sp}_t$ in complex rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06463 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation Theory of the Twisted Yangians in Complex Rank Kannan, Arun S. Kanungo, Shihan Representation Theory In 2016, Etingof defined the notion of a Yangian in a symmetric tensor category and posed the problem to study them in the context of Deligne categories. This problem was studied by Kalinov in 2020 for the Yangian $Y(\mathfrak{gl}_t)$ of the general linear Lie algebra $\mathfrak{gl}_t$ in complex rank using the techniques of ultraproducts. In particular, Kalinov classified the simple finite-length modules over $Y(\mathfrak{gl}_t)$. In this paper, we define the notion of a twisted Yangian in Deligne's categories, and we extend these techniques to classify finite-length simple modules over the twisted Yangians $Y(\mathfrak{o}_t)$ and $Y(\mathfrak{sp}_t)$ of the orthogonal and symplectic Lie algebras $\mathfrak{o}_t,\mathfrak{sp}_t$ in complex rank. |
| title | Representation Theory of the Twisted Yangians in Complex Rank |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2505.06463 |