Multiplicity One Theorem of Branching Laws,
Lie Groups and Representation Theory Seminar, the University of Tokyo, Japan, 18 December 2001.

It is notorious that the multiplicity in the branching law is often infinite when we restrict an irreducible unitary representation to a non-compact subgroup (even though it is a maximal subgroup). However, for unitary highest weight modules, we can present a geometric condition for multiplicity to be one. It turns out that our criterion implies various known classical multiplicity one results, and also gives some new results both for finite and infinite dimensional representation theory.


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© Toshiyuki Kobayashi