Local Theta Lift of Whittaker Models associated to Nilpotent Orbits

by Dr Raul Gomez (National University of Singapore, Singapore)

Wednesday 17 Apr 2013, 16:00 → 17:30 Asia/Kolkata

AG-69 (Colaba Campus)

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.