New simple modules for the $W$-algebra $W(2,2)$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913888105136128 |
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| author | Chen, Hongjia Xu, Dashu |
| author_facet | Chen, Hongjia Xu, Dashu |
| contents | 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 $Ω(λ,α,h)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New simple modules for the $W$-algebra $W(2,2)$ Chen, Hongjia Xu, Dashu Representation Theory 17B10, 17B68 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 $Ω(λ,α,h)$ 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. |
| title | New simple modules for the $W$-algebra $W(2,2)$ |
| topic | Representation Theory 17B10, 17B68 |
| url | https://arxiv.org/abs/2506.08794 |