Theta Correspondence and the Orbit Method

Explore the intersection of theta correspondence and the orbit method in this 45-minute lecture from the International Mathematical Union. Delve into the powerful theory of theta correspondence, initiated by R. Howe, for constructing irreducible admissible representations of classical groups over local fields. Examine the orbit method introduced by A. A. Kirillov for describing irreducible unitary representations of Lie groups through coadjoint orbits. Investigate the implications of Howe's theory on the orbit method and unitary representation theory, with a particular focus on recent work by Barbasch, Ma, and the speakers regarding the construction and classification of special unipotent representations of real classical groups. Access accompanying slides for a comprehensive visual aid to the lecture's content.