Generalized Dolbeault Sequences in Parabolic Geometry

In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model G/P of a Cartan geometry.The first operator in this sequence is closely related to the Dirac operator in k Clifford variables, D = (D 1 , . . ., D k ), whereWe describe the structure of these sequences in case the dimension n is odd.It follows from the construction that all these operators are invariant with respect to the action of the group G .These results are obtained by constructing homomorphisms of generalized Verma modules, which are purely algebraic objects.