*Branching Problems of Unitary Representations*,

"Perspectives in Representation Theory"
Strategic Workshop and Round
Table Discussion (organized by
Steffen Koenig, Henning Krause, Peter Littelmann, and Gunter Malle),

Physikzentrum Bad Honnef, Germany, 7-9 July 2006.

The branching problem asks how a given irreducible representation
of a group decomposes when restricted to a subgroup.
Making an observation on wild features of branching problems of unitary
representations for non-compact subgroups, we address the question of
finding a criterion for discreteness of spectrum and finiteness of
multiplicities in the irreducible decomposition of the restriction of
reductive Lie groups.

Applications to other areas of mathematics such as topology of locally
symmetric spaces, and global analysis on indefinite-Riemannian homogeneous
spaces will be illustrated.

© Toshiyuki Kobayashi