Global analysis by hidden symmetry
  Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects:   (A) global analysis on X by using representations of G (hidden symmetry);   (B) global analysis on X by using representations of G';   (C) branching laws of representations of G when restricted to the subgroup G'.   We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting when $X_C$ is $G_C$-spherical. Applications to branching problems of unitary representations, and to spectral analysis on pseudo-Riemannian locally symmetric spaces are also discussed. 
Toshiyuki Kobayashi
math.RT math-ph math.DG math.MP