Poincaré series for non-Riemannian locally symmetric spaces

DOI10.1016/j.aim.2015.08.029zbMath1333.53073arXiv1209.4075OpenAlexW1518598821WikidataQ102447919 ScholiaQ102447919MaRDI QIDQ895542

Toshiyuki Kobayashi, Fanny Kassel

Publication date: 3 December 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4075

zbMATH Keywords

Laplace-Beltrami operatordiscrete spectrumreductive symmetric spacepseudo-Riemannian manifoldlocally symmetric spaceproperly discontinuous actioninvariant differential operatordiscrete series representationgeneralized Poincaré seriesClifford-Klein form

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Semisimple Lie groups and their representations (22E46) Discrete subgroups of Lie groups (22E40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Differential geometry of symmetric spaces (53C35)

Related Items (17)

Intrinsic Sound of Anti-de Sitter Manifolds ⋮ Spectrum of semisimple locally symmetric spaces and admissibility of spherical representations ⋮ Invariant differential operators on spherical homogeneous spaces with overgroups ⋮ Counting problems for special-orthogonal Anosov representations ⋮ Conjectures on Reductive Homogeneous Spaces ⋮ Four-dimensional compact Clifford–Klein forms of pseudo-Riemannian symmetric spaces with signature (2, 2) ⋮ Poincaré series for non-Riemannian locally symmetric spaces ⋮ Counting orbits of certain infinitely generated non-sharp discontinuous groups for the anti-de Sitter space ⋮ Unexpected spectral asymptotics for wave equations on certain compact spacetimes ⋮ Spectral analysis on pseudo-Riemannian locally symmetric spaces ⋮ Obstructions to the existence of compact Clifford–Klein forms for tangential symmetric spaces ⋮ Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds ⋮ Wave front sets of reductive Lie group representations. III. ⋮ On semisimple standard compact Clifford-Klein forms ⋮ Linear independence of generalized Poincaré series for anti-De Sitter 3-manifolds ⋮ A restriction on proper group actions on homogeneous spaces of reductive type ⋮ A quantitative study of orbit counting and discrete spectrum for anti-de Sitter 3-manifolds

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