Representations of Hamiltonian Lie algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915688992473088 |
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| author | Futorny, Vyacheslav Tantubay, Santanu |
| author_facet | Futorny, Vyacheslav Tantubay, Santanu |
| contents | We consider the Shen-Larsson functor from the category of modules for the symplectic Lie algebra $\s$ to the category of modules for the Hamiltonian Lie algebra and show that it preserves the irreducibility except in the finite number of cases. The obtained irreducible modules for the Hamiltonian Lie algebra are cuspidal, whose weight multiplicities equal the dimension of the corresponding module of the symplectic Lie algebra. This extends well-known results for other Cartan type Lie algebras to the Hamiltonian case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representations of Hamiltonian Lie algebras Futorny, Vyacheslav Tantubay, Santanu Representation Theory 17B10, 17B65, 17B66 We consider the Shen-Larsson functor from the category of modules for the symplectic Lie algebra $\s$ to the category of modules for the Hamiltonian Lie algebra and show that it preserves the irreducibility except in the finite number of cases. The obtained irreducible modules for the Hamiltonian Lie algebra are cuspidal, whose weight multiplicities equal the dimension of the corresponding module of the symplectic Lie algebra. This extends well-known results for other Cartan type Lie algebras to the Hamiltonian case. |
| title | Representations of Hamiltonian Lie algebras |
| topic | Representation Theory 17B10, 17B65, 17B66 |
| url | https://arxiv.org/abs/2503.00749 |