## *Multiplicities in the Restriction and Real Spherical Varieties*.
Representations
of Reductive Groups (organized by Jeff Adams, Peter Trapa, and David Vogan Jr.). Salt Lake City, USA, 8-12 July 2013.

Branching problems ask how irreducible representations of groups
decompose when restricted to subgroups. Decompositions of tensor product
representations, Littlewood-Richardson's rules, and Blattner formulae are
classical examples of branching laws for symmetric pairs. However, we
observe that bad features like ''infinite multiplicites” may well happen in
dealing with branching problems of irreducible representations of real
reductive groups *G* when restricted to maximal reductive subgroups *G*', even
if (*G*,*G*') are symmetric pairs. In this talk I plan to discuss what is a
''nice framework” in which we could ecpect to develop a fruitful and
detailed analysis on branching laws. In connection with the theory of ''real
spherical varieties”, I plan to give a classification of reductive
symmetric pairs (*G*,*G*') for which multiplicites are always finite/bounded,
respectively.

© Toshiyuki Kobayashi