Tempered Representations and Nilpotent Orbits

Abstract

Given a nilpotent orbit O of a real, reductive algebraic group, a necessary condition is given for the existence of a tempered representation pi such that O occurs in the wave front cycle of pi. The coefficients of the wave front cycle of a tempered representation are expressed in terms of volumes of precompact submanifolds of an affine space.Comment: The class of nilpotent orbits studied in this paper is different from the class of noticed nilpotent orbits studied by Noel. A previous version of this paper erroneously stated that these two classes are the same. Representation Theory, Volume 16, 201