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.

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, 2012