##### Department of Mathematics,

University of California San Diego

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### Representation Theory Seminar

## Atsushi Ichino

#### Osaka City University and University of Toronto

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

##### Abstract:

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

Host: Wee Teck Gan

### December 5, 2006

### 1:30 PM

### AP&M 7218

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