##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Bertram Kostant

#### MIT

## Geometric quantization and the emergence of the five exceptional groups

##### Abstract:

In contrast to Marsden-Weinstein reduction we introduce the notion of symplectic induction that raises dimensions rather than lowering them. We show that the symplectic induction of certain coadjoint orbits of a Lie group $G$ lead to coadjoint orbits of a larger group. In particular, coadjoint orbits of the five exceptional groups arise from certain coadjoint orbits of classical groups. For example, Tits-Koecher machinary associates to certain Jordan algebras coadjoint orbits of a compact Lie compact classical group. The split forms of $E_{6}$. $E_{7}$ and $E_{8}$ arise, respectively, from the symplectic induction of the coadjoint orbits associated to rank 1 Joradan algebras over the reals, complexes and quaternions.

Host: Nolan Wallach

### February 24, 2005

### 3:00 PM

### AP&M 6438

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