Generalized affine buildings for semisimple algebraic groups over real closed fields

Abstract

We use real algebraic geometry to construct an affine $\hat{I}›$-building $B$ associated to the $\mathbb{F}$-points of a semisimple algebraic group, where $\mathbb{F}$ is a valued real closed field. We characterize the spherical building at infinity and the local building at a base point. We compute stabilizers of various subsets of $B$ and obtain group decompositions.

74 pages, 10 figures, accepted for publication in Munster Journal of Mathematics