Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbicurves
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910392157995008 |
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| author | Gao, Xu Liu, Jianqi Zhu, Yiyi |
| author_facet | Gao, Xu Liu, Jianqi Zhu, Yiyi |
| contents | In this paper, we introduce a notion of twisted restricted conformal blocks on totally ramified orbicurves and establish an isomorphism between the space of twisted restricted conformal blocks and the space of twisted conformal blocks. The relationships among twisted (restricted) conformal blocks, $g$-twisted (restricted) correlation functions, and twisted intertwining operators are explored. Furthermore, by introducing a geometric generalization of Zhu's algebra and its modules, we obtain a description of the space of coinvariants by modules over associative algebras and show it is finite-dimensional under some conditions. In particular, a more conceptual proof of the $g$-twisted fusion rules theorem in vertex operator algebra theory is provided. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_00545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbicurves Gao, Xu Liu, Jianqi Zhu, Yiyi Algebraic Geometry Mathematical Physics Quantum Algebra 17B69, 81T40, 14H30 In this paper, we introduce a notion of twisted restricted conformal blocks on totally ramified orbicurves and establish an isomorphism between the space of twisted restricted conformal blocks and the space of twisted conformal blocks. The relationships among twisted (restricted) conformal blocks, $g$-twisted (restricted) correlation functions, and twisted intertwining operators are explored. Furthermore, by introducing a geometric generalization of Zhu's algebra and its modules, we obtain a description of the space of coinvariants by modules over associative algebras and show it is finite-dimensional under some conditions. In particular, a more conceptual proof of the $g$-twisted fusion rules theorem in vertex operator algebra theory is provided. |
| title | Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbicurves |
| topic | Algebraic Geometry Mathematical Physics Quantum Algebra 17B69, 81T40, 14H30 |
| url | https://arxiv.org/abs/2403.00545 |