Propagation of multiplicity-freeness property for holomorphic vector bundles
arXiv:math/0607004 · doi:10.1007/978-1-4614-7193-6_6
Abstract
We give a complete proof of a propagation theorem of multiplicity-free property from fibers to spaces of global sections for holomorphic vector bundles. The propagation theorem is formalised in three ways, aiming for producing various multiplicity-free theorems in representation theory for both finite and infinite dimensional cases in a systematic and synthetic manner. The key geometric condition in our theorem is an orbit-preserving anti-holomorphic diffeomorphism on the base space, which brings us to the concept of visible actions on complex manifolds.
final version
References in corpus (4)
- Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs
- Visible actions on symmetric spaces
- Restrictions of generalized Verma modules to symmetric pairs
- A generalized Cartan decomposition for the double coset space U(n_1) x U(n_2) x U(n_3)) U(n) / U(p) x U(q)
Cited by in corpus (9)
- Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs
- A program for branching problems in the representation theory of real reductive groups
- F-method for symmetry breaking operators
- Differential symmetry breaking operators. I-Genreal theory and F-method. II-Rankin-Cohen Operators for Symmetric Pairs
- Construction of Intertwining Operators between Holomorphic Discrete Series Representations
- Conformal symmetry breaking on differential forms and some applications
- Conformally covariant differential symmetry breaking operators for a vector bundle of rank 3 over S^3
- Multiplicity-free representations and coisotropic actions of certain nilpotent Lie groups over quasi-symmetric Siegel domains
- Recent advances in branching problems of representations