Abstract:The aim of the first part of a series of papers is to give a description of invariant differential operators on manifolds with an almost Hermitian symmetric structure of the type $G/B$ which are defined on bundles associated to the reducible but undecomposable representation of the parabolic subgroup $B$ of the Lie group $G$. One example of an operator of this type is the Penrose's local twistor transport. In this part general theory is presented, and conformally invariant operators are studied in more details.
Keywords: invariant operators, Cartan connection, almost hermitian symmetric structures
AMS Subject Classification: 58G35, 53C10