##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Petar Bakic

#### Utah

## Howe Duality for Exceptional Theta Correspondences

##### Abstract:

The theory of local theta correspondence is built up from two main ingredients: a reductive dual pair inside a symplectic group, and a Weil representation of its metaplectic cover. Exceptional correspondences arise similarly: dual pairs inside exceptional groups can be constructed using so-called Freudenthal Jordan algebras, while the minimal representation provides a suitable replacement for the Weil representation. The talk will begin by recalling these constructions. Focusing on a particular dual pair, we will explain how one obtains Howe duality for the correspondence in question. Finally, we will discuss applications of these results. The new work in this talk is joint with Gordan Savin.

### January 27, 2022

### 2:00 PM

Pre-talk at 1:20 PM

APM 6402 and Zoom;

See https://www.math.ucsd.edu/~nts

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