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