2010/03/15 by Annette Werner, Werner, Annette
Computer Science · Mathematics · #14T05 #20E42 #20G25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Polynomial and algebraic computation #math.AG #math.GR #msc:14T05 #msc:20E42 #msc:20G25
paper · pdf · doi:10.48550/arxiv.1003.2966
This paper is a generalization of arXiv:0905.3293 to arbitrary semisimple groups
arxiv created 2010/03/15 · openalex publication_date 2010/03/15 · arxiv updated 2010/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation and that it is related to the tropicalization of the hypersurface given by the character of the representation.