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arXiv · 2506.08794

New simple modules for the $W$-algebra $W(2,2)$

Hongjia Chen·Dashu Xu
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Abstract

In this paper, we construct a novel class of simple modules for the $W$-algebra $W(2,2)$. Our approach involves taking tensor products of finitely many non-weight simple modules $\Omega(\lambda,\alpha,h)$ with an arbitrary simple restricted module. We provide a necessary and sufficient condition for these modules to be simple, and subsequently determine their isomorphism classes. Through a comparative analysis with other known simple modules in the literature, we establish that these constructed modules are generically new.

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BibTeXRIS

Hongjia Chen, Dashu Xu. 2025-06-10. New simple modules for the $W$-algebra $W(2,2)$. https://arxiv.org/abs/2506.08794

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