I am studying the representation theory of Lie groups from the viewpoint of analysis. My aim is to compute inner products or operators explicitly by realizing representations on explicit function spaces. By explicit computation, we can determine the dependence on the parameter, and it is expected that we can capture the behavior of the representation at singular parameters, which is difficult to know from general theory. Recently I am interested in determining the operators arising from the restriction of representations of Lie groups to subgroups, and studying this problem when the representation is realized on the function space on a “Hermitian symmetric space” or a “symmetric R space”, by using tools such as “Jordan algebras”.