Report
Explicit realization of bounded modules for symplectic Lie algebras: spinor versus oscillator
| العنوان: | Explicit realization of bounded modules for symplectic Lie algebras: spinor versus oscillator |
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| المؤلفون: | Futorny, Vyacheslav, Grantcharov, Dimitar, Ramirez, Luis Enrique, Zadunaisky, Pablo |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, 17B10, 16G99 |
| الوصف: | 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. Comment: 24 pages, minor corrections made |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.15929 |
| رقم الانضمام: | edsarx.2406.15929 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |