Compactifications of Bruhat-Tits buildings associated to linear representations

Abstract

Let G be a connected semisimple group over a non-Archimedean local field. For every faithful, geometrically irreducible linear representation of G we define a compactification of the associated Bruhat-Tits building X(G). This yields a finite family of compactifications of X(G) which contains the polyhedral compactification. Moreover, this family can be regarded as a non-Archimedean analogue of Satake compactifications for symmetric spaces.