ON THE QUANTIZATION OF SPHERICAL NILPOTENT ORBITS

Let G be the real symplectic group Sp(2n, R). This paper determines the global sections of certain line bundles over the spherical nilpotent K-C-orbit O. As a consequence, Vogan's conjecture for these orbits is verified. The conjecture holds that there exists a unique unitary (g, K)-module structure on the space of the algebraic global sections of the line bundle associated to the admissible datum, provided that the boundary partial derivative(O) over bar has complex codimension at least 2 in (O) over bar. Similar results are obtained for the metaplectic twofold cover Mp(2n, R) of Sp(2n, R).