Let $G$ be a semisimple Lie group. The term Borel subgroup refers to a maximal connected solvable subgroup of $G$. A parabolic subgroup of $G$ is a Lie subgroup containing some Borel subgroup.
The set of all proper parabolic subgroups of $G$ with reverse inclusion forms a poset, which has the structure of a simplicial complex and a spherical building. This is the Tits building $\Delta(G)$.
I want to get a feeling for $\Delta(G)$. Is there a nice instructive example where I can understand what the parabolic subgroups are and visualize the simplicial complex $\Delta(G)$?
For example for $G= SL(2,\mathbb{R})$, I know that two parabolic subgroups are given by $$ B^+ = \left\{\begin{pmatrix} * & * \\ 0 & *\end{pmatrix} \in SL(2,\mathbb{R})\right\}, \qquad\quad B^- = \left\{\begin{pmatrix} * & 0 \\ * & *\end{pmatrix} \in SL(2,\mathbb{R})\right\}. $$ Can one see the appartments (Coxeter complexes) here?