Explicit realization of bounded modules for symplectic Lie algebras: spinor versus oscillator
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913630777245696 |
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| author | Futorny, Vyacheslav Grantcharov, Dimitar Ramirez, Luis Enrique Zadunaisky, Pablo |
| author_facet | Futorny, Vyacheslav Grantcharov, Dimitar Ramirez, Luis Enrique Zadunaisky, Pablo |
| contents | We provide an explicit combinatorial realization of all simple and injective (hence, and projective) modules in the category of bounded $\mathfrak{sp}(2n)$-modules. This realization is defined via a natural tableaux correspondence between spinor-type modules of $\mathfrak{so}(2n)$ and oscillator-type modules of $\mathfrak{sp}(2n)$. In particular, we show that, in contrast with the $A$-type case, the generic and bounded $\mathfrak{sp}(2n)$-modules admit an analog of the Gelfand-Graev continuation from finite-dimensional representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit realization of bounded modules for symplectic Lie algebras: spinor versus oscillator Futorny, Vyacheslav Grantcharov, Dimitar Ramirez, Luis Enrique Zadunaisky, Pablo Representation Theory 17B10, 16G99 We provide an explicit combinatorial realization of all simple and injective (hence, and projective) modules in the category of bounded $\mathfrak{sp}(2n)$-modules. This realization is defined via a natural tableaux correspondence between spinor-type modules of $\mathfrak{so}(2n)$ and oscillator-type modules of $\mathfrak{sp}(2n)$. In particular, we show that, in contrast with the $A$-type case, the generic and bounded $\mathfrak{sp}(2n)$-modules admit an analog of the Gelfand-Graev continuation from finite-dimensional representations. |
| title | Explicit realization of bounded modules for symplectic Lie algebras: spinor versus oscillator |
| topic | Representation Theory 17B10, 16G99 |
| url | https://arxiv.org/abs/2406.15929 |