## Periods Over Spherical Subgroups: An Extension of Some of the Langlands Conjectures

Periods of automorphic forms over spherical subgroups tend to: (1) distinguish images of functorial lifts and (2) give information about L-functions.

This raises the following questions, given a spherical variety X=H\G: Locally, which irreducible representations admit a non-zero H-invariant functional or, equivalently, appear in the space of functions on X? Globally, can the period over H of an automorphic form on G be related to some L-value?