Tensor structure on the module category of the triplet superalgebra $\mathcal{SW}(m)$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913629293510656 |
|---|---|
| author | Nakano, Hiromu |
| author_facet | Nakano, Hiromu |
| contents | We discuss the tensor structure on the category of modules of the $N=1$ triplet vertex operator superalgebra $\mathcal{SW}(m)$ introduced by Adamović and Milas. Based on the theory of vertex tensor supercategories, we determine the structure of fusion products between the simple and projective $\mathcal{SW}(m)$-modules and show that the tensor supercategory on $\mathcal{SW}(m)$-mod is rigid. Technically, explicit solutions of a fourth-order Fuchsian differential equation are important to show the rigidity of $\mathcal{SW}(m)$-modules. We construct solutions of this Fuchsian differential equation using the theory of the Dotsenko-Fateev integrals developed by Sussman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20898 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor structure on the module category of the triplet superalgebra $\mathcal{SW}(m)$ Nakano, Hiromu Quantum Algebra Mathematical Physics Representation Theory 17B69, 18D10, 81R10, 81T40 We discuss the tensor structure on the category of modules of the $N=1$ triplet vertex operator superalgebra $\mathcal{SW}(m)$ introduced by Adamović and Milas. Based on the theory of vertex tensor supercategories, we determine the structure of fusion products between the simple and projective $\mathcal{SW}(m)$-modules and show that the tensor supercategory on $\mathcal{SW}(m)$-mod is rigid. Technically, explicit solutions of a fourth-order Fuchsian differential equation are important to show the rigidity of $\mathcal{SW}(m)$-modules. We construct solutions of this Fuchsian differential equation using the theory of the Dotsenko-Fateev integrals developed by Sussman. |
| title | Tensor structure on the module category of the triplet superalgebra $\mathcal{SW}(m)$ |
| topic | Quantum Algebra Mathematical Physics Representation Theory 17B69, 18D10, 81R10, 81T40 |
| url | https://arxiv.org/abs/2412.20898 |