Radon transforms for quasi-equivariant D-modules on generalized flag manifolds

Abstract

In this paper we deal with Radon transforms for generalized flag manifolds in the framework of quasi-equivariant D-modules. We shall follow the method employed by Baston-Eastwood and analyze the Radon transform using the Bernstein-Gelfand-Gelfand resolution and the Borel-Weil-Bott theorem. We shall determine the transform completely on the level of the Grothendieck groups. Moreover, we point out a vanishing criterion and give a sufficient condition in order that a D-module associated to an equivariant locally free O-module is transformed into an object of the same type. The case of maximal parabolic subgroups of classical simple groups is studied in detail.