论文标题
仿型建筑物中的非椭圆网和凸集
Non-elliptic Webs and Convex Sets in the Affine Building
论文作者
论文摘要
我们描述了$ \ Mathfrak SL_3 $非椭圆网的非纤维网络，以仿射建筑物的凸集。 Kuperberg在他在排名中的工作中定义了非椭圆形的网络基础。$ 2 $蜘蛛类别。 Fontaine，Kamnitzer，Kuperberg表明，$ \ Mathfrak Sl_3 $非椭圆网对猫（0）三角构造的磁盘是双重的。我们表明，每个这样的三角形磁盘都是建筑物中通用多边形的最小凸和max-convex船体的相交。从Satake纤维的每个组件中选择一个通用多边形会产生非纤细的网络基础。正如Joswig，Sturmfels，Yu和Zhang在工作中讨论的那样，Aggine Building中的凸壳首先是由Faltings引入的，并且与热带凸度有关。
We describe the $\mathfrak sl_3$ non-elliptic webs in terms of convex sets in the affine building. Kuperberg defined the non-elliptic web basis in his work on rank-$2$ spider categories. Fontaine, Kamnitzer, Kuperberg showed that the $\mathfrak sl_3$ non-elliptic webs are dual to CAT(0) triangulated diskoids in the affine building. We show that each such triangulated diskoid is the intersection of the min-convex and max-convex hulls of a generic polygon in the building. Choosing a generic polygon from each of the components of the Satake fiber produces the non-elliptic web basis. The convex hulls in the affine building were first introduced by Faltings and are related to tropical convexity, as discussed in work by Joswig, Sturmfels, Yu and by Zhang.
