ADMISSIBLE NILPOTENT COADJOINT ORBITS OF p-ADIC REDUCTIVE LIE GROUPS

The orbit method conjectures a close relationship between the set of irreducible unitary representations of a Lie group G, and admissible coadjoint orbits in the dual of the Lie algebra. We define admissibility for nilpotent coadjoint orbits of p-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples. We find that for unitary, symplectic, orthogonal, general linear and special linear groups over p-adic fields, the admissible nilpotent orbits coincide with the so-called special orbits defined by Lusztig and Spaltenstein in connection with the Springer correspondence.