Note on a theorem of H. Moscovici

AbstractLet Γ be a discrete subgroup of a semisimple Lie group G such that ΓβG has a finite volume. Using a theorem of Moscovici we express the multiplicity of discrete series representations of G in the discrete spectrum of L2(ΓβG) as the L2-index of a twisted Dirac operator. This result, which extends a result of Moscovici and of the author, holds for all integrable discrete series and for infinitely many nonintegrable discrete series. In particular, up to computing L2-indices in the special rank one case, it implies the Osborne-Warner formula