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arXiv · 2406.15929

Explicit realization of bounded modules for symplectic Lie algebras: spinor versus oscillator

Vyacheslav Futorny·Dimitar Grantcharov·Luis Enrique Ramirez·Pablo Zadunaisky
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Abstract

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.

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Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramirez, Pablo Zadunaisky. 2024-06-22. Explicit realization of bounded modules for symplectic Lie algebras: spinor versus oscillator. https://arxiv.org/abs/2406.15929

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