Representations of Super Yangians with Gelfand-Tsetlin bases
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911628228820992 |
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| author | Futorny, Vyacheslav Li, Zheng Zhang, Jian |
| author_facet | Futorny, Vyacheslav Li, Zheng Zhang, Jian |
| contents | The evaluation homomorphisms from the super Yangian $\Ymn$ to the universal enveloping algebra $\U(\gl_{m|n})$ allows one to regard the covariant tensor module of $\gl_{m|n}$ as $\Ymn$ modules. We study simple quotients of the submodules generated by a tensor product of highest weight vectors inside the tensor products of covariant evaluation modules. In the case $n=0$, this recover all finite-dimensional simple modules of $\Y(\mathfrak{gl}_m)$. We give a necessary and sufficient condition for such modules to be tame, which generalizes the earlier work of Nazarov and Tarasov for $\Y(\mathfrak{gl}_m)$ to the super case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Representations of Super Yangians with Gelfand-Tsetlin bases Futorny, Vyacheslav Li, Zheng Zhang, Jian Representation Theory Quantum Algebra The evaluation homomorphisms from the super Yangian $\Ymn$ to the universal enveloping algebra $\U(\gl_{m|n})$ allows one to regard the covariant tensor module of $\gl_{m|n}$ as $\Ymn$ modules. We study simple quotients of the submodules generated by a tensor product of highest weight vectors inside the tensor products of covariant evaluation modules. In the case $n=0$, this recover all finite-dimensional simple modules of $\Y(\mathfrak{gl}_m)$. We give a necessary and sufficient condition for such modules to be tame, which generalizes the earlier work of Nazarov and Tarasov for $\Y(\mathfrak{gl}_m)$ to the super case. |
| title | Representations of Super Yangians with Gelfand-Tsetlin bases |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2604.25462 |