Resonances of the d'Alembertian on the anti-de Sitter space SO e ( 2 , 2 ) / SO e ( 2 , 1 ) $\mathop {\rm {SO_e}}(2,2)/\mathop {\rm {SO_e}}(2,1)$

Abstract

We consider the action of the d'Alembertian on functions on the pseudo-Riemannian three-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.