Compactifications of Bruhat‐Tits buildings associated to linear representations

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. In addition, this family can be seen as a non‐Archimedean analogue of the family of Satake compactifications for symmetric spaces.