The linear $\SL_2(\Z)$-action on $\T^n$: ergodic and von Neumann algebraic aspects

Paul Jolissaint, Alain Valette

The unique irreducible representation of $\SL_2(\R)$ on ${\mathbb{R}}^n$ induces an action, called the \textit{linear action}, of $\SL_2(\Z)$ on the torus $\T^n$ for every $n\ge 2$. For $n$…