Title: Geometric Satake, dense orbits, and transfers of invariants
Speaker: Joshua Kiers - OSU
Abstract: We begin by recalling some highlights from the Geometric Satake correspondence, connecting the geometry of the affine Grassmannian for a complex connected semisimple group to the representation theory of the Langlands dual group. Next, we describe three elementary applications, each of which is a new proof of a well-known result in representation theory: the Clebsch-Gordon rule, the PRV conjecture, and Wahl's conjecture. Inspired by these examples, we ask two hopeful questions: one on the existence of dense orbits in cyclic convolution varieties, and the other on a representation-theoretic relationship between two groups whose Langlands duals are embedded one inside the other.
Seminar Link: https://research.math.osu.edu/agseminar/
