Conformal symmetry breaking operators for anti-de sitter spaces

Abstract

For a pseudo-Riemannian manifold X and a totally geodesic hypersurface Y, we consider the problem of constructing and classifying all linear differential operators ℰi (X) → ℰj (Y) between the spaces of differential forms that intertwine multiplier representations of the Lie algebra of conformal vector fields. Extending the recent results in the Riemannian setting by Kobayashi–Kubo–Pevzner [Lecture Notes in Math. 2170, (2016)], we construct such differential operators and give a classification of them in the pseudo-Riemannian setting where both X and X are of constant sectional curvature, illustrated by the examples of anti-de Sitter spaces and hyperbolic spaces.