We prove an analogue of the Sato-Tate conjecture for Drinfeld modules. Using ideas of Drinfeld, J.-K. Yu showed that Drinfeld modules satisfy some Sato-Tate law, but did not describe the actual law. More precisely, for a Drinfeld module φ defined over a field L, he constructs a continuous representation ρ∞ : WL → D× of the Weil group of L into a certain division algebra, which encodes the Sato-...

This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P , where G is a real or complex semisimple Lie group and P ⊂ G is a parabolic subgroup. We use methods from differential geometry and very elementary finite–dimensional representation theory to construct sequences of invariant differential operators for such geometries, both in the smooth and the holomor...