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 E i (X) → 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.
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Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner. Conformal symmetry breaking operators for anti-de Sitter spaces. Trends in Mathermatics, 2018, Geometric Methods in Physics, XXXV, pp.22 - 70. 〈https://www.springer.com/gp/book/9783319635934〉. 〈hal-01907080〉

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