##### Department of Mathematics,

University of California San Diego

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### Representation Theory

## Nolan Wallach

#### UCSD

## Exceptional spherical triples

##### Abstract:

Let G be a connected, simply connected, simple group over the complex numbers. Let K be the fixed point group of an involutive automorphism of G and let P be a parabolic subgroup of G such that KP has interior in G. Then we say that (G,K,P) is a spherical triple if there is a Borel subgroup of K, B, such that B has an open orbit in G/P. This condition is equivalent with having (degenerate) principal series for the non-compact real form corresponding to K be multiplicity free. In this talk we will give a classification of these triples for the exceptional groups.

Host:

### April 13, 2004

### 2:30 PM

### AP&M 7218

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