T. Kobayashi. Propagation of multiplicity-free property for holomorphic vector bundles. In A. Huckleberry, I. Penkov, and G. Zuckerman, editors, Lie Groups: Structure, Actions, and Representations (In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday), Vol. 306 of Progress in Mathematics. 2013. 32 pp. ISBN: 978-1-4614-7192-9. arXiv:math/0607004..

We prove a propagation theorem of multiplicity-free property from fibers to spaces of global sections for holomorphic vector bundles, which yields various multiplicity-free results in representation theory for both finite and infinite dimensional cases.

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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