Global regularity and solvability of left-invariant differential systems on compact Lie groups.

We are interested in global properties of systems of left-invariant differential operators on compact Lie groups: regularity properties, properties on the closedness of the range and finite dimensionality of their cohomology spaces, when acting on various function spaces, e.g., smooth, analytic and Gevrey. Extending the methods of Greenfield and Wallach (Trans Am Math Soc 183:153–164, 1973) to systems, we obtain abstract characterizations for these properties and use them to derive some generalizations of results due to Greenfield (Proc Am Math Soc 31:115–118, 1972), Greenfield and Wallach (Proc Am Math Soc 31:112–114, 1972), as well as global versions of a result of Caetano and Cordaro (Trans Am Math Soc 363(1):185–201, 2011) for involutive structures. [ABSTRACT FROM AUTHOR]