Multiplicity-free Representations and Visible Actions on Complex Manifolds

Abstract

mulas §1.5. Multiplicity-free representations — definition §2. Multiplicity-free theorem — general framework §2.1. Holomorphic bundles and anti-holomorphic maps §2.2. Multiplicity-free theorem — line bundle case §2.3. Geometry on the base space D §2.4. Multiplicity-free theorem — vector bundle case §3. Visible actions on complex manifolds §3.1. Previsible and visible actions on complex manifolds §3.2. Infinitesimal characterization for visible actions §3.3. Anti-holomorphic map §4. Coisotropic actions, polar actions, and visible actions §4.1. Coisotropic actions on symplectic manifolds §4.2. Polar actions on Riemannian manifolds §4.3. Actions on Kahler manifolds §4.4. Visible actions and multiplicity-free representations