Abstract:BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called $K$-types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing in BGG sequences, are described.
Keywords: BGG sequences, invariant differential operators, branching rules, $K$-types, complexes, homogeneous spaces
AMS Subject Classification: 35P15, 43A85, 22E46