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Discrete spectrum of the Laplacian on non-Riemannian locally symmetric spaces Fanny Kassel

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Discrete spectrum of the Laplacian on non-Riemannian locally symmetric spaces

Fanny Kassel

Abstract: The spectrum of the Laplacian has been extensively studied on Riemann- ian manifolds, and particularly Riemannian locally symmetric spaces. Toshiyuki Kobayashi and I have considered similar problems for non-Riemannian locally sym- metric spaces. I will explain our results in the case of anti-de Sitter 3-manifolds, i.e. Lorentzian 3-manifolds of constant negative curvature. In this case, spectral theory relies on a good understanding of the geometry of proper actions of discrete subgroups of SL2(R)×SL2(R) on SL2(R) (by left and right multiplication), and there are interesting links with the representation theory of surface groups into SL2(R).

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