School of Mathematics Seminars and Lectures
Dual groups of spherical varieties and an extension of the Langlands conjectures
by Prof. Yiannis Sakellaridis (Rutgers University, USA)
Monday, January 16, 2012
from
to
(Asia/Kolkata)
at Colaba Campus ( A-369 )
at Colaba Campus ( A-369 )
Description |
Spherical varieties form a wide class of interesting (almost) homogeneous spaces for reductive groups, which includes symmetric spaces, flag varieties and others. If $X=H\backslash G$ is such a variety, the problem of distinction asks when does an irreducible representation $\pi$ of $G(k)$, where $k$ is a local field, appear in the space of functions on $X$; and globally, for which automorphic representations of $G$ is the period integral over an orbit of $H$ non-zero. \\ I will explain how one attaches a dual group to a spherical variety (following Gaitsgory and Nadler, and later work of Venkatesh and myself, all based on results of Brion, Knop and others). And how this dual group answers (conjecturally) some of the above questions, in a way that generalizes some of the Langlands conjectures (which correspond to the spherical variety $X=H, G=H \times H$). |