Local Theta Lift of Whittaker Models associated to Nilpotent Orbits

ABSTRACT:
Let $(G,\tilde{G})$ be a dual pair in the stable range, with $G$ being the
smaller member. Given a nilpotent orbit $\mathcal(O)\subset
\mathfrak{g}=Lie(G)$, we can associate to it a nilpotent orbit
$\Theta(\mathcal{O})\subset \tilde{\mathfrak{g}} = Lie(\tilde{G})$. Let
$(\pi,V)$ be an irreducible representation of $G$. In this talk we explore
the relationship between $Wh_{\mathcal{O}}(\pi)$, the space of Whittaker
models of $(\pi,V)$ associated to $\mathcal{O}$ and
$Wh_{\Theta(\mathcal{O})}(\Theta(\pi))$, where $\Theta(\pi)$ is the "big"
theta-lift of $\pi$.

The talk will be aimed at non-experts. In particular, some time will be
spent discussing what the nilpotent orbits in classical groups are, and
how they "theta lift" to other classical groups.