仿射建筑的Kostant凸性
Kostant Convexity for affine buildings
摘要：
证明了Kostants凸性定理在仿射厚建筑物上的一个类似定理，并给出了它在具有仿射BN-对的群上的一个应用。回想一下，仿射建筑有两个自然回缩到固定的公寓A上：回缩r以A中的凹室为中心，回缩$ρ$以无穷远处的球形建筑中的一个房间为中心。我们证明了对于A中的每个特殊顶点x，集合$ρ(r^{-1}(W.x))$是W. x的某个凸包.证明可以减少到一个关于Coxeter复形的陈述，并严重依赖于代数群的最高权表示的特征公式。
英文摘要：
We prove an analogue of Kostants convexity theorem for thick affine buildings and give an application for groups with affine BN-pair. Recall that there are two natural retractions of the affine building onto a fixed apartment A: The retraction r centered at an alcove in A and the retraction $ρ$ centered at a chamber in the spherical building at infinity. We prove that for each special vertex x in A the set $ρ(r^{-1}(W.x))$ is a certain convex hull of W.x. The proof can be reduced to a statement about Coxeter complexes and heavily relies on a character formula for highest weight representations of algebraic groups.
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