Propagation of multiplicity-free property for holomorphic vector
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
32 pp. ISBN: 978-1-4614-7192-9.
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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© Toshiyuki Kobayashi