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Simple 𝔰𝔩(V)-modules which are free over an abelian subalgebra

  • Jonathan Nilsson ORCID logo EMAIL logo
Published/Copyright: May 3, 2023

Abstract

Let 𝔭 be a parabolic subalgebra of 𝔰 𝔩 ( V ) of maximal dimension and let 𝔫 𝔭 be the corresponding nilradical. In this paper, we classify the set of 𝔰 𝔩 ( V ) -modules whose restriction to U ( 𝔫 ) is free of rank 1. It turns out that isomorphism classes of such modules are parametrized by polynomials in dim V - 1 variables. We determine the submodule structure for these modules and we show that they generically are simple.

MSC 2020: 17B10; 17B45; 16G99

Communicated by Jan Frahm


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Received: 2022-08-26
Revised: 2022-12-19
Published Online: 2023-05-03
Published in Print: 2023-09-01

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