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This thesis is concerned with the theory of invariant bilinear differentialpairings on parabolic geometries. It introduces the concept formally with thehelp of the jet bundle formalism and provides a detailed analysis. Moreprecisely, after introducing the most important notations and definitions, wefirst of all give an algebraic description for pairings on homogeneous spacesand obtain a first existence theorem. Next, a classification of first orderinvariant bilinear differential pairings is given under exclusion of certaindegenerate cases that are related to the existence of invariant lineardifferential operators. Furthermore, a concrete formula for a large class ofinvariant bilinear differential pairings of arbitrary order is given and manyexamples are computed. The general theory of higher order invariant bilineardifferential pairings turns out to be much more intricate and a generalconstruction is only possible under exclusion of finitely many degenerate caseswhose significance in general remains elusive (although a result for projectivegeometry is included). The construction relies on so-called splitting operatorsexamples of which are described for projective geometry, conformal geometry andCR geometry in the last chapter.

Invariant Bilinear Differential Pairings on Parabolic Geometries