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arXiv · 2508.05917

Quasi-Whittaker modules

Cunguang Cheng·Wenting Gao·Shiyuan Liu·Kaiming Zhao·Yueqiang Zhao
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Abstract

In this paper, a general setting is proposed to define a class of modules over nonsemisimple Lie algebras $\mathfrak{g}$ induced by a nonperfect ideal $\mathfrak{p}$. This class of Lie algebras includes many well-known Lie algebras, and some of this class of modules are Whittaker modules and others are not. We call these modules quasi-Whittaker modules. By introducing a new concept: the Whittaker annihilator for universal quasi-Whittaker modules, we are able to determine the necessary and sufficient conditions for the irreducibility of the universal quasi-Whittaker modules. In the reducible case, we can obtain some maximal submodules. In particular, we classify the irreducible quasi-Whittaker modules for many Lie algebras, and obtain a lot of irreducible smooth $\mathcal{W}_n^+$-modules of height $2$.

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BibTeXRIS

Cunguang Cheng, Wenting Gao, Shiyuan Liu, Kaiming Zhao, Yueqiang Zhao. 2025-08-08. Quasi-Whittaker modules. https://arxiv.org/abs/2508.05917

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