Isotropic geometry and twistors in higher dimensions. I. The generalized Klein correspondence and spinor flags in even dimensions

Abstract

An equivariant diffeomorphism is given between flag varieties of totally isotropic subspaces of a complex inner product space and certain orbits under the complex spin group within flag varieties of the associated spinor modules. This allows a generalization of the Klein correspondence underlying twistor theory, applicable to arbitrary (even) dimensional conformally compactified Minkowski space and its isotropic subspaces.