Type $\textrm{II}$ quantum subgroups for quantum $\mathfrak{sl}_N$. $\textrm{II}$: Classification
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917742075969536 |
|---|---|
| author | Edie-Michell, Cain Gannon, Terry |
| author_facet | Edie-Michell, Cain Gannon, Terry |
| contents | In this paper we study the indecomposable module categories over $\mathcal{C}(\mathfrak{sl}_N, k)$, the category of integrable level-$k$ respresentations of affine Kac-Moody $\mathfrak{sl}_N$. Our first main result classifies these module categories in the case of generic $k$, i.e. $k$ is sufficiently large relative to $N$. As $\mathcal{C}(\mathfrak{sl}_N, k)$ is a braided tensor category, there is a relative tensor product structure on its category of module categories. In the generic setting we obtain a formula for the relative tensor product rules between the indecomposable module categories. Our second main result classifies the indecomposable module categories over $\mathcal{C}(\mathfrak{sl}_N, k)$ for $N\leq 7$, with no restrictions on $k$. In this non-generic setting, exceptional module categories are obtained. This work relies heavily on previous results by the two authors. In previous literature, module category classification results were known only for $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Type $\textrm{II}$ quantum subgroups for quantum $\mathfrak{sl}_N$. $\textrm{II}$: Classification Edie-Michell, Cain Gannon, Terry Quantum Algebra Category Theory Representation Theory In this paper we study the indecomposable module categories over $\mathcal{C}(\mathfrak{sl}_N, k)$, the category of integrable level-$k$ respresentations of affine Kac-Moody $\mathfrak{sl}_N$. Our first main result classifies these module categories in the case of generic $k$, i.e. $k$ is sufficiently large relative to $N$. As $\mathcal{C}(\mathfrak{sl}_N, k)$ is a braided tensor category, there is a relative tensor product structure on its category of module categories. In the generic setting we obtain a formula for the relative tensor product rules between the indecomposable module categories. Our second main result classifies the indecomposable module categories over $\mathcal{C}(\mathfrak{sl}_N, k)$ for $N\leq 7$, with no restrictions on $k$. In this non-generic setting, exceptional module categories are obtained. This work relies heavily on previous results by the two authors. In previous literature, module category classification results were known only for $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$. |
| title | Type $\textrm{II}$ quantum subgroups for quantum $\mathfrak{sl}_N$. $\textrm{II}$: Classification |
| topic | Quantum Algebra Category Theory Representation Theory |
| url | https://arxiv.org/abs/2408.02794 |