Winfried Frisch
On the Bruhat-Tits-Building of Unitary Groups: Simultaneous Diagonalization of Real Norms
Preprint series: TMathematica Gottingensis

MSC:

20G25 Linear algebraic groups over local fields and their integers

11E57 Classical groups

Abstract: Let $K$ be a local field and $G$ the group of $K$-rational
points of an unitary group over $K$. In Bruhat F., Tits J.,
Sch\'emas en groupes et immeubles des groupes classique
sur un corps local {II}: groupes unitaires, Bull. Soc. Math
France 115 (1987), 141-195, there is given a
concrete interpretation of the Bruhat-Tits-building of $G$
as a space of ``maximinorant'' norms on the vector space
associated to the natural representation of $G$. I describe
a method to find for any given two points in this building
an apartment, that contains both of them.
Keywords: classical groups, Bruhat-Tits-buildings, p-adic Lie-groups