论文标题
$ \ text {sl} _ {2k+1} $的三角形演示和倾斜模块
Triangle presentations and tilting modules for $\text{SL}_{2k+1}$
论文作者
论文摘要
三角形演示文稿是有限的投影几何形状上的组合结构，这些几何形式表征了在本地有限的$ \ tilde {\ text {a}} _ {n-1} $（$ n \ ge3 $）的本地有限建筑物的顶点。从类型$ \ tilde {\ text {a}} _ {n-1} $三角形表示$ q $的几何形式中，我们在图表单类别$ \ text {web} {web}（web}（\ text {sl） $ p \ ge n-1 $，使得$ q \ equiv 1 $ mod $ p $。当$ \ mathbb {k} $被代数关闭并且$ n $奇数时，这为$ \ text {sl} _ {n} $的倾斜模块类别提供了新的光纤函子。
Triangle presentations are combinatorial structures on finite projective geometries which characterize groups acting simply transitively on the vertices of a locally finite building of type $\tilde{\text{A}}_{n-1}$ ($n\ge3$). From a type $\tilde{\text{A}}_{n-1}$ triangle presentation on a geometry of order $q$, we construct a fiber functor on the diagrammatic monoidal category $\text{Web}(\text{SL}^{-}_{n})$ over any field $\mathbb{k}$ with characteristic $p\ge n-1$ such that $q \equiv 1$ mod $p$. When $\mathbb{k}$ is algebraically closed and $n$ odd, this gives new fiber functors on the category of tilting modules for $\text{SL}_{n}$.
