  Let $G$ be a nilpotent, connected, simply connected Lie group with Lie
algebra $\mathfrak g$, and $\pi$ a unitary representation of $G$. The goal is
to prove that the wave front set of $\pi$ coincides with the asymptotic cone of
the orbital support of $\pi$, i.e.
$\mathrm{WF}(\pi)=\mathrm{AC}(\bigcup_{\sigma\in \mathrm{supp}(\pi)}\mathcal
O_\sigma)$, where $\mathcal O_\sigma\subset i\mathfrak g^\ast$ is the coadjoint
orbit associated to the irreducible unitary representation $\sigma\in \hat{G}$
by Kirillov.
