Propagation of multiplicity-freeness property for holomorphic vector bundles. (English) Zbl 1284.32011
Huckleberry, Alan (ed.) et al., Lie groups: structure, actions, and representations. In honor of Joseph A. Wolf on the occasion of his 75th birthday. New York, NY: Birkhäuser/Springer (ISBN 978-1-4614-7192-9/hbk; 978-1-4614-7193-6/ebook). Progress in Mathematics 306, 113-140 (2013).
Summary: We give a complete proof of a propagation theorem of the multiplicity-free property from fibers to spaces of global sections of holomorphic vector bundles. The propagation theorem is formulated 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.
For the entire collection see [Zbl 1276.00017].
For the entire collection see [Zbl 1276.00017].
MSC:
| 32M10 | Homogeneous complex manifolds |
| 32M05 | Complex Lie groups, group actions on complex spaces |
| 22E46 | Semisimple Lie groups and their representations |
| 32L05 | Holomorphic bundles and generalizations |
Keywords:
multiplicity-free representation; unitary representation; homogeneous space; holomorphic bundleReferences:
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