Kostant Convexity for affine buildings

2007/01/03 by Petra Schwer, Schwer, Petra · 1 citation
Mathematics · #20E42 #20G25 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Mathematical and Theoretical Analysis #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.math/0701094

openalex publication_date 2007/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Alcove walks, buildings, symmetric functions and representations

Cited by

• Non-discrete affine buildings and convexity

Related

• Non-discrete affine buildings and convexity
• Property (T) for groups acting on affine buildings
• Generalized affine buildings
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