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Algebraic Geometry and Representation Theory Seminar

WednesdayJan 19, 202217:00
Algebraic Geometry and Representation Theory Seminar
Speaker:Petar BakicTitle:Howe duality for exceptional theta correspondencesAbstract:opens in new windowin html    pdfopens in new windowThe seminar will be held only in zoom: https://weizmann.zoom.us/j/98304397425
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.