On Quaternionic Representations and Exceptional Theta Lifts

Explore quaternionic representations and their crucial role in exceptional theta correspondences through this 59-minute conference lecture. Examine the exceptional Lie groups of type E_6, E_7, and E_8 with forms of split rank 4 that admit quaternionic structure, focusing on how each contains a dual pair G x G' where G is of type G_2 and G' has split rank 1. Learn how restricting the minimal representation of the ambient group to this dual pair creates an exceptional theta correspondence where quaternionic representations in the sense of Gross-Wallach become essential. Review the fundamental properties of quaternionic representations and discover how these key characteristics enable the establishment of new results about exceptional theta correspondences. Gain insights into applications within automorphic forms and functorial liftings, drawing from collaborative research with H.-Y. Loke and G. Savin presented at the Workshop on "Eisenstein Series, Spaces of Automorphic Forms, and Applications" at the Erwin Schrödinger International Institute for Mathematics and Physics.