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 ${\mathcal{E}}^i(X)\to {\mathcal{E}}^j(Y)$ 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.

18 pages