##### Department of Mathematics,

University of California San Diego

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### Representation Theory Seminar

## Luis Lomeli

#### University of Iowa

## The Langlands-Shahidi Method for the Split Classical Groups over Function Fields and Functoriality

##### Abstract:

The Langlands-Shahidi method over a global function field will be presented for the split classical groups. We will highlight the difficulties that arise in positive characteristic with local-global arguments. Important applications to functoriality for generic representations of the split classical groups to an appropriate GL(N) are then obtained when the Langlands-Shahidi method is used together with a converse of Cogdell and Piatetski-Shapiro. Finally, we will mention how to go from the weak functorial lift to the strong lift. This has an important application to the Ramanujan conjecture, due to the fact that it is a theorem of Lafforgue for GL(N).

Host: Wee Teck Gan

### October 28, 2008

### 2:30 PM

### AP&M 7321

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