10/4/2007

Atsushi Ichino
Institute for Advanced Study

On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture

A period of an automorphic form on a reductive group G over a number field is defined by its integral over a subgroup H of G. Such periods are often related to special values of automorphic L-functions. In this talk, we present a conjecture in the case of special orthogonal groups, which can be regarded as a refinement of the global Gross-Prasad conjecture about the restriction of automorphic representations of SO(n+1) to SO(n). If time permits, we also discuss a relation of our conjecture to Arthur's conjecture on the multiplicity of representations in the space of automorphic forms. This is a joint work with Tamotsu Ikeda.