School of Mathematics Seminars and Lectures
Local Theta Lift of Whittaker Models associated to Nilpotent Orbits
by Dr. Raul Gomez (National University of Singapore, Singapore)
Wednesday, April 17, 2013
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-69 )
at Colaba Campus ( AG-69 )
Description |
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. |