Branching problems ask how irreducible representations of groups G decompose when restricted to subgroups G'. We present a program on branching problems, from abstract feature to concrete construction of symmetry breaking operators.
As an abstract feature, we provide a geometric criterion on the pair of reductive groups for the multiplicities of the branching laws to be always of finite (more strongly, uniformly bounded) by using analysis on (real) spherical varieties.
As a concrete construction of symmetry breaking operators (SBOs), we explain an idea of the F-method in constructing differential SBOs. Finally, we discuss some classification results of all non-local and local SBOs by an example.
© Toshiyuki Kobayashi