##### Department of Mathematics,

University of California San Diego

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### Representation Theory

## Ralf Schmidt

#### University of Oklahoma

## Local newforms on $GSp(4)$

##### Abstract:

This talk is about a theory of local newforms for irreducible, admissible representations of the group $GSp(4,F)$, where $F$ is a non-archimedean local field. We will present a joint work with Brooks Roberts, where we proved the existence of a local newform theory analogous to Casselman's theory for $GL(2,F)$. A key feature of our theory is to consider fixed vectors under a family of open-compact subgroups called the paramodular groups. Local newforms provide a link between classical modular forms and automorphic representations. Our theory therefore has applications to Siegel modular forms of degree $2$; this will be discussed in a talk by Brooks Roberts.

Host: K. Baur

### February 1, 2005

### 2:00 PM

### AP&M 7218

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