On the Moore Formula of Compact Nilmanifolds

Let G be a connected and simply connected two-step nilpotent Lie group and Γ a lattice subgroup of G. In this note, we give a new multiplicity formula, according to the sense of Moore, of irreducible unitary representations involved in the decomposition of the quasi-regular representation Ind_Γ^G(1). Extending then the Abelian case.