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Propagation of multiplicity-freeness property for holomorphic vector bundles

Toshiyuki Kobayashi
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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.

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BibTeXRIS

Toshiyuki Kobayashi. 2006-06-30. Propagation of multiplicity-freeness property for holomorphic vector bundles. https://doi.org/10.1007/978-1-4614-7193-6_6

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