Global analysis by hidden symmetry

Abstract

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.

Special volume in honor of Roger Howe on the occasion of his 70th birthday

References in corpus (1)

• Invariant differential operators on spherical homogeneous spaces with overgroups

Cited by in corpus (6)

• A criterion for discrete branching laws for Klein four symmetric pairs and its application to $E_{6(-14)}$
• Admissible restrictions of irreducible representations of reductive Lie groups: symplectic geometry and discrete decomposability
• Spectral analysis on pseudo-Riemannian locally symmetric spaces
• Discretely decomposable restrictions of $(\mathfrak{g},K)$-modules for Klein four symmetric pairs of exceptional Lie groups of Hermitian type
• A hidden symmetry of a branching law
• Recent advances in branching problems of representations