论文标题
$ a_n $ Web类别的模块类别来自$ \ tilde {a} _ {n-1} $ - 建筑物
Module categories for $A_n$ web categories from $\tilde{A}_{n-1}$-buildings
论文作者
论文摘要
我们在本地有限的$ \ tilde {a} _ {n-1} $ building $δ$的顶点上配备了向量捆绑包的类别，而在正面特征上，$ a_ {n} $网的结构是模块类别的结构。此模块类别是$ rep（sl_ {n}）$ actoce bundles上的$ q $ -Analogue，上面是$ sl_n $ stright lattice。我们表明，我们的模块类别相对于建筑物的对称性是均等的，当组$ g $仅在$δ$的顶点进行过渡时，这会恢复琼斯构建的光纤函数。
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.
