## *Multiplicities in the Decomposition of Unitary Representations
of Reductive Lie Groups*.

Lie Groups, Algebraic Groups and Transformation Groups: A conference
in honor of Ernest B. Vinberg's 70th birthday (organized by Herbert
Abels, Vladimir Chernousov, Gregory Margulis, Detlev Poguntke, and Katrin
Tent). Universität Bielefeld, Germany, 20-24 July 2007.

In a celebrated paper by
É. A. Vinberg and B. N. Kimelfeld (1978),
a geometric characterization in terms of flag varieties
was proved for the multiplicities of
finite dimensional irreducible representations
occurring in the induced/restricted representations
to be not greater than one.
Unlike the finite dimensional case,
multiplicities are often infinite
in the irreducible decompositions
for **infinite dimensional** representations,
even in (seemingly) natural settings.
In this talk, I plan to discuss
finite multiplicity theorems and multiplicity-free
theorems,
in particular, for unitary
representations
as a descendant of Vinberg-Kimelfeld's work.

[

programme ]

© Toshiyuki Kobayashi