$\mathfrak{so}_n(\mathbb{C})$-modules which are free over an abelian nilradical

Yang Chen; Haijun Tan; Lu Zhang

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arXiv · 2607.11100

$\mathfrak{so}_n(\mathbb{C})$-modules which are free over an abelian nilradical

Yang Chen·Haijun Tan·Lu Zhang

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Abstract

In this paper, we classify the category of $\mathfrak{so}_n(\mathbb{C})$-modules whose restrictions to the universal enveloping algebra of the abelian nilradical of a maximal parabolic subalgebra are free of rank $1$. We show that they generically are simple, and give an explicit description of submodules in the non-simple case. This category embodies a certain connection between weight modules and non-weight modules.

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Yang Chen, Haijun Tan, Lu Zhang. 2026-07-13. $\mathfrak{so}_n(\mathbb{C})$-modules which are free over an abelian nilradical. https://arxiv.org/abs/2607.11100

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