For any irrational number h, let A be the corresponding Weyl algebra over Z^{2g} and consider the ergodic group of automorphisms of A induced by the action of Sp(2g, Z) on Z^{2g}. We show that the only Sp(2g, Z)-invariant state on A is tracial. This is a joint project with Federico Bambozzi and Nicola Pinamonti