Branching problems ask how irreducible representations ƒÎ of groups G ''decompose” when restricted to subgroups G'. For real reductive groups, branching problems include various important special cases, however, it is notorious that ''infinite multiplicites” may well happen in general even if (G,G') are natural pairs such as symmetric pairs. By using analysis on (real) spherical varieties, we explain a general project on branching pborlems (K- 2014), a necessary and sufficient condition on the pair of reductie groups for the multiplicities to be always finite (and also to be of uniformly bounded) (K-T.Oshima, 2013)), and its classfication results (K-Matsuki, 2014)). I give a classification of all symmetry breaing operators that intertwines two spherical principal series representations of two groups O(n+1,1) to O(n,1). The last part is a joint work with B. Speh (to appear in Memoirs of AMS).
© Toshiyuki Kobayashi