Module categories for $A_n$ web categories from $\tilde{A}_{n-1}$-buildings
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911770387415040 |
|---|---|
| author | McGovern, Emily |
| author_facet | McGovern, Emily |
| contents | We equip the category of vector bundles over the vertices of a locally finite $\tilde{A}_{n-1}$ building $Δ$ with the structure of a module category over a category of type $A_{n}$ webs in positive characteristic. This module category is a $q$-analogue of the $Rep(SL_{n})$ action on vector bundles over the $sl_n$ weight lattice. We show our module categories are equivariant with respect to symmetries of the building, and when a group $G$ acts simply transitively on the vertices of $Δ$ this recovers the fiber functors constructed by Jones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01149 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Module categories for $A_n$ web categories from $\tilde{A}_{n-1}$-buildings McGovern, Emily Quantum Algebra We equip the category of vector bundles over the vertices of a locally finite $\tilde{A}_{n-1}$ building $Δ$ with the structure of a module category over a category of type $A_{n}$ webs in positive characteristic. This module category is a $q$-analogue of the $Rep(SL_{n})$ action on vector bundles over the $sl_n$ weight lattice. We show our module categories are equivariant with respect to symmetries of the building, and when a group $G$ acts simply transitively on the vertices of $Δ$ this recovers the fiber functors constructed by Jones. |
| title | Module categories for $A_n$ web categories from $\tilde{A}_{n-1}$-buildings |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2211.01149 |