Smooth representations of affine Kac-Moody algebras
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912678563282944 |
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| author | Futorny, Vyacheslav Guo, Xiangqian Xue, Yaohui Zhao, Kaiming |
| author_facet | Futorny, Vyacheslav Guo, Xiangqian Xue, Yaohui Zhao, Kaiming |
| contents | Smooth modules for affine Kac-Moody algebras have a prime importance for the quantum field theory as they correspond to the representations of the universal affine vertex algebras. But, very little is known about such modules beyond the category of positive energy representations. We construct a new class of smooth modules over affine Kac-Moody algebras. In a particular case, these modules are isomorphic to those induced from generalized Whittaker modules for Takiff Lie algebras. We establish the irreducibility criterion for constructed modules in the case of the affine sl(2) Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smooth representations of affine Kac-Moody algebras Futorny, Vyacheslav Guo, Xiangqian Xue, Yaohui Zhao, Kaiming Representation Theory Mathematical Physics 17B10, 17B67, 17B69 Smooth modules for affine Kac-Moody algebras have a prime importance for the quantum field theory as they correspond to the representations of the universal affine vertex algebras. But, very little is known about such modules beyond the category of positive energy representations. We construct a new class of smooth modules over affine Kac-Moody algebras. In a particular case, these modules are isomorphic to those induced from generalized Whittaker modules for Takiff Lie algebras. We establish the irreducibility criterion for constructed modules in the case of the affine sl(2) Lie algebra. |
| title | Smooth representations of affine Kac-Moody algebras |
| topic | Representation Theory Mathematical Physics 17B10, 17B67, 17B69 |
| url | https://arxiv.org/abs/2404.03855 |