Generalized Bernstein--Reznikov integrals

Abstract

We find a closed formula for the triple integral on spheres in ${\mathbb{R}}^{2n}\times {\mathbb{R}}^{2n}\times {\mathbb{R}}^{2n}$ whose kernel is given by powers of the standard symplectic form. This gives a new proof to the Bernstein--Reznikov integral formula in the $n=1$ case. Our method also applies for linear and conformal structures.

Cited by in corpus (11)

• Finite multiplicity theorems for induction and restriction
• A program for branching problems in the representation theory of real reductive groups
• F-method for symmetry breaking operators
• Classification of finite-multiplicity symmetric pairs
• Shintani functions, real spherical manifolds, and symmetry breaking operators
• Estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles
• Extensions of the classical theorems for very well-poised hypergeometric functions
• Real double flag varieties for the symplectic group
• Double Gegenbauer expansion of $|s-t{|}^{\alpha }$
• Recent advances in branching problems of representations
• Generating operators of symmetry breaking -- from discrete to continuous