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