Injectivity of the Double Fibration Transform for Cycle Spaces of Flag Domains

Abstract. The basic setup consists of a complex flag manifold Z = G/Q where G is a complex semisimple Lie group and Q is a parabolic subgroup, an open orbit D = G0(z) ⊂ Z where G0 is a real form of G, and a G0 – homogeneous holomorphic vector bundle E → D. The topic here is the double fibration transform P: Hq(D;O(E)) → H0(MD;O(E′)) where q is given by the geometry of D, MD is the cycle space of D, and E ′ → MD is a certain naturally derived holomorphic vector bundle. Schubert intersection theory is used to show that P is injective whenever E is sufficiently negative