## 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.

[ arXiv |
RIMS preprint(pdf) |
RIMS preprint(ps.gz) |
preprint version(pdf) |
preprint version(dvi) |
SpringerLink |
related papers ]

© Toshiyuki Kobayashi