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Let $G$ be a real, reductive algebraic group, and let $X$ be a homogeneousspace for $G$ with a non-zero invariant density. We give an explicitdescription of a Zariski open, dense subset of the asymptotics of the temperedsupport of $L^2(X)$. Under additional hypotheses, this result remains true forvector bundle valued harmonic analysis on $X$. These results follow from anupper bound on the wave front set of an induced Lie group representation undera uniformity condition.

Wave Front Sets of Reductive Lie Group Representations III