point $x$ of the building an affinoid subgroup ${\rm G}_x$, which is characterized by a unique maximal point $\vartheta(x)$ in the ambient analytic space of the group. The map $\vartheta$ is a closed embedding when the ground field is local; a compactification is obtained when $\vartheta$ is composed with the (analytic map) associated to a fibration from the group to one of its flag varieties. One obtains in this way the finite family of compactifications described in [@Wer07]. One nice feature is the possibility to obtain easily maps between compactifications of a given group but attached to distinct flag varieties. This enables one to understand in combinatorial Lie-theoretic terms which boundary components are shrunk when going from a “big” compactification to a smaller one.

The second way mimics I. Satake’s work in the real case. More precisely, it uses a highest weight representation of the group in order to obtain a map from the building of the group to the building of the general linear group of the representation space which, as we said before, is nothing else than a space of non-Archimedean norms. Then it remains to use the seminorm compactification mentioned above by taking the closure of the 