 
Summary: Previous Up Next Article
Citations
From References: 2
From Reviews: 0
MR2441254 (2010d:22026) 22E50 (11F85 14M17)
Sakellaridis, Yiannis (ILTLAV)
On the unramified spectrum of spherical varieties over padic fields. (English summary)
Compos. Math. 144 (2008), no. 4, 9781016.
The notion of a distinguished representation acquires importance primarily because distinguished
representations often characterize images of Langlands functorial lifts. Questions related to distin
guished representations include computing the multiplicity of the space of invariant linear forms,
investigating whether or not the period integral is factorizable, and how distinction affects arith
metic invariants like Lfunctions. These and similar questions have been extensively studied in the
past two decades or so.
However, what is not very satisfactory is the lack of a general picture, with most of the work in
the area focusing on special cases. Of late, there have been some serious attempts to understand
the general picture in this context, especially the work of Sakellaridis and SakellaridisVenkatesh.
The essence of their work is to do harmonic analysis on spherical varieties over padic fields and
to understand this in terms of a dual group that appears in the geometric Langlands programme.
In the automorphic setting, these studies have found applications in the GrossPrasad conjecture
