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arXiv · 2505.15273

Non-weight modules over gap-$p$ Virasoro algebras

Chengkang Xu·Fulin Chen·Shaobin Tan
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Abstract

In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal Whittaker modules to be irreducible and study the structure of irreducible Whittaker modules. The $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 are classified and the irreducibility of such modules are determined. Moreover, the irreducibility of tensor products of $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 and irreducible restricted modules is also determined.

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Chengkang Xu, Fulin Chen, Shaobin Tan. 2025-05-21. Non-weight modules over gap-$p$ Virasoro algebras. https://arxiv.org/abs/2505.15273

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