Type III actions on boundaries of ${\tilde{A}}_n$ buildings

Let $\mathrm{\Gamma }$ be a group of type rotating automorphisms of a building $\text{fX}$ of type ${\tilde{A}}_n$ and order $q$. Suppose that $\text{G}$ acts freely and transitively on the vertex set of $\text{fX}$. Then the action of $\mathrm{\Gamma }$ on the boundary of $\text{fX}$ is ergodic, of type $\text{tq}$ or type $\text{tqs}$ depending on whether $n$ is odd or even.