Representations of the super-Yangian of type $D(n,m)$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910870892707840 |
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| author | Molev, A. I. |
| author_facet | Molev, A. I. |
| contents | We consider the classification problem for finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak{osp}}_{2n|2m}$ with $n\geqslant 2$. We give necessary conditions for an irreducible highest weight representation to be finite-dimensional. We conjecture that these conditions are also sufficient and prove the conjecture for a class of representations with linear highest weights. The arguments are based on a new type of odd reflections for the Yangian associated with ${\frak{osp}}_{2|2}$. In the Appendix, we construct an isomorphism between the Yangians associated with the Lie superalgebras ${\frak{osp}}_{2|2}$ and ${\frak{gl}}_{1|2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representations of the super-Yangian of type $D(n,m)$ Molev, A. I. Representation Theory Mathematical Physics Quantum Algebra We consider the classification problem for finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak{osp}}_{2n|2m}$ with $n\geqslant 2$. We give necessary conditions for an irreducible highest weight representation to be finite-dimensional. We conjecture that these conditions are also sufficient and prove the conjecture for a class of representations with linear highest weights. The arguments are based on a new type of odd reflections for the Yangian associated with ${\frak{osp}}_{2|2}$. In the Appendix, we construct an isomorphism between the Yangians associated with the Lie superalgebras ${\frak{osp}}_{2|2}$ and ${\frak{gl}}_{1|2}$. |
| title | Representations of the super-Yangian of type $D(n,m)$ |
| topic | Representation Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2407.00076 |