Resonances of the d'Alembertian on the Anti-de Sitter space $\mathrm{S}{\mathrm{O}}_{\mathrm{e}}(2,2)/\mathrm{S}{\mathrm{O}}_{\mathrm{e}}(2,1)$

Abstract

We consider the action of the d'Alembertian on the functions on the pseudo-Riemannian 3-dimensional Anti-de Sitter space. We determine the resonances of this operator. With each resonance one can associate a residue representation. We give an explicit description of these representations via Langlands parameters.