Boris Doubrov, Bifiltered Parabolic Geometries

We introduce the notion of a bifiltered manifold and generalizing the constructions of the symbol and Tanaka prolongation from nilpotent differential geometry. Next, we consider bifiltered manifolds modeled by bigradings of simple Lie algebras and show how this generalizes known constructions in the parabolic geometries such as existence of a unique normal Cartan connection. Finally, we show how the language of bifiltered manifolds can be used for uniform treatment of correspondence spaces in parabolic geometries, where the covering space is not necessarily regular in the classical sense.