Propagation of multiplicity-freeness property for holomorphic vector bundles

Details Propagation of multiplicity-freeness property for holomorphic vector bundles Propagation of multiplicity-freeness property for holomorphic vector bundles

2006-06-30

arxiv.org/abs/math/0607004v2

Mathematics

Representation Theory

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Scientific paper

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.

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