Simple 𝔰𝔩(V)-modules which are free over an abelian subalgebra
| Autor: | Jonathan Nilsson |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Forum Mathematicum. |
| ISSN: | 1435-5337 0933-7741 |
| DOI: | 10.1515/forum-2022-0245 |
| Popis: | Let 𝔭 {\mathfrak{p}} be a parabolic subalgebra of 𝔰 𝔩 ( V ) {\mathfrak{sl}(V)} of maximal dimension and let 𝔫 ⊂ 𝔭 {\mathfrak{n}\subset\mathfrak{p}} be the corresponding nilradical. In this paper, we classify the set of 𝔰 𝔩 ( V ) {\mathfrak{sl}(V)} -modules whose restriction to U ( 𝔫 ) {U(\mathfrak{n})} is free of rank 1. It turns out that isomorphism classes of such modules are parametrized by polynomials in dim V - 1 {\dim V-1} variables. We determine the submodule structure for these modules and we show that they generically are simple. |
| Databáze: | OpenAIRE |
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