BIMSA > Algebraic and Complex Geometry Seminar Penrose transformations of automorphic cohomology groups on flag domains
Penrose transformations of automorphic cohomology groups on flag domains
Organizer
Dali Shen
Speaker
Yang Shen
Time
Tuesday, October 28, 2025 4:00 PM - 5:30 PM
Venue
Online
Online
Zoom 242 742 6089 (BIMSA)
Abstract
In this talk, I will present recent joint work with Kefeng Liu on the Penrose transformation of automorphic cohomology groups of homogeneous line bundles on flag domains. We construct the Penrose transforms explicitly and identify the geometric and representation-theoretic conditions under which the Penrose transforms are isomorphisms. As an application, we show that higher automorphic cohomology groups of certain line bundles on non-classical flag domain are canonically isomorphic to spaces of automorphic forms on Hermitian symmetric domains. We also propose the problem concerning the arithmetic structure of totally degenerate limits of discrete series (TDLDS) on non-classical flag domains, pointing to further connections with geometric representation theory and Hodge theory.