Available via WWW.ESI.AC.AT SPECIAL INVARIANT OPERATORS I.

Abstract. The aim of the rst part of a series of papers is to give a description of invariant dierential operators on manifolds with an almost Hermitian symmetric structure of the type G/B which are dened 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. 1. Introduction. There is a series of papers by R.Baston, M.Eastwood, T.Bailey and others de-scribing invariant operators on manifolds with almost Hermitian symmetric struc-ture (AHS- structure) (see [Baston I,II,1991]) of the type G/B acting on bundles associated to a reducible, but indecomposable representation of B