Unipotent representations attached to spherical nilpotent orbits

A coadjoint nilpotent orbit [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] of a complex semisimple Lie group G is said to be spherical if it contains an open orbit of a Borel subgroup. We determine when and how to attach unitary representations to such an orbit for the real orthogonal and symplectic groups. Our results actually extend to a larger class of nilpotent coadjoint orbits.