Gelfand-Tsetlin modules for Lie algebras of rank $2$
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913641833431040 |
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| author | Anđelić, Milica da Fonseca, Carlos M. Futorny, Vyacheslav Tsylke, Andrew |
| author_facet | Anđelić, Milica da Fonseca, Carlos M. Futorny, Vyacheslav Tsylke, Andrew |
| contents | We explicitly construct families of simple modules for Lie algebras of rank $2$, on which certain commutative subalgebra acts diagonally and has a simple spectrum. In type $A$ these modules are well known generic Gelfand-Tsetlin modules and they can be viewed as such for other rank $2$ Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gelfand-Tsetlin modules for Lie algebras of rank $2$ Anđelić, Milica da Fonseca, Carlos M. Futorny, Vyacheslav Tsylke, Andrew Representation Theory 17B10 We explicitly construct families of simple modules for Lie algebras of rank $2$, on which certain commutative subalgebra acts diagonally and has a simple spectrum. In type $A$ these modules are well known generic Gelfand-Tsetlin modules and they can be viewed as such for other rank $2$ Lie algebras. |
| title | Gelfand-Tsetlin modules for Lie algebras of rank $2$ |
| topic | Representation Theory 17B10 |
| url | https://arxiv.org/abs/2402.00483 |