-modules which are free over an abelian nilradical
arXiv:2607.11100
summary
The paper classifies so_n(C)-modules that become free rank‑1 modules over the universal enveloping algebra of the abelian nilradical of a maximal parabolic subalgebra, showing they are generically simple and describing submodules in the non‑simple cases.
Abstract
In this paper, we classify the category of -modules whose restrictions to the universal enveloping algebra of the abelian nilradical of a maximal parabolic subalgebra are free of rank . 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.
Topics & keywords
#lie algebras#parabolic subalgebras#weight modules#non-weight modules#universal enveloping algebraso_n(C)abelian nilradicalmaximal parabolic subalgebrafree rank 1 modulesmodule classification