Representations of the super-Yangian of type $B(n,m)$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911953073471488 |
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| author | Molev, Alexander Ragoucy, Eric |
| author_facet | Molev, Alexander Ragoucy, Eric |
| contents | We are concerned with finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak osp}_{2n+1|2m}$. Every such representation is highest weight and we use embedding theorems and odd reflections of Yangian type to derive necessary conditions for an irreducible highest weight representation to be finite-dimensional. We conjecture that these conditions are also sufficient. We prove the conjecture in the case $n=1$ and arbitrary $m\geqslant 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12479 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Representations of the super-Yangian of type $B(n,m)$ Molev, Alexander Ragoucy, Eric Representation Theory Mathematical Physics Quantum Algebra We are concerned with finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak osp}_{2n+1|2m}$. Every such representation is highest weight and we use embedding theorems and odd reflections of Yangian type to derive necessary conditions for an irreducible highest weight representation to be finite-dimensional. We conjecture that these conditions are also sufficient. We prove the conjecture in the case $n=1$ and arbitrary $m\geqslant 1$. |
| title | Representations of the super-Yangian of type $B(n,m)$ |
| topic | Representation Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2311.12479 |