Conformal symmetry breaking operators for anti-de Sitter spaces

TL;DR

This paper constructs and classifies conformal symmetry breaking differential operators between differential forms on anti-de Sitter spaces and their hypersurfaces, extending previous Riemannian results to pseudo-Riemannian settings.

Contribution

It extends the classification of conformal symmetry breaking operators to pseudo-Riemannian manifolds of constant curvature, including anti-de Sitter spaces.

Findings

Constructed explicit differential operators intertwining conformal vector fields.

Provided a classification of these operators in the anti-de Sitter and hyperbolic space settings.

Extended Riemannian symmetry breaking results to pseudo-Riemannian geometry.

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 $\mathcal{E}^i(X) \to \mathcal{E}^j(Y)$ 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 $Y$ are of constant sectional curvature, illustrated by the examples of anti-de Sitter spaces and hyperbolic spaces.