Visible Actions on Complex Manifolds and Multiplicity-free Theorems,
(2 lectures), International Symposium on Representation Theory and Automorphic Forms, Seoul National University, Seoul, Republic of Korea, 14-17 February 2005.

Based on the Lie group action on a complex manifold such that its generic orbits intersect with a totally real submanifold, we give multiplicity-free theorems of representations realized on holomorphic vector bundles.

A number of multiplicity-free examples will be presented, including finite and infinite dimensional representations; classical and some new cases; and discrete and continuous spectrum.

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© Toshiyuki Kobayashi