Propagation Theorem of Multiplicity-Free Representations and
Visible Actions on Complex Manifolds.
AMS 2008 Spring Southeastern Meeting. Louisiana State University,
Baton Rouge, USA, 28-30 March 2008.
In this talk, I plan to present a simple principle that produces various multiplicity-free theorems for both finite and infinite dimensional representations (possibly, with continuous spectrum).
The main idea is to find under what assumption on group actions on holomorphic vector bundles, the multiplicityfree property propagates from fibers to sections. The underlying geometry is explained as ''visible actions'' on complex manifolds.
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© Toshiyuki Kobayashi