Let G=SO0​(1,n) be the conformal group acting on the (n−1) dimensional
sphere S, and let (πλ​)λ∈C​ be the spherical
principal series. For generic values of λ=(λ1​,λ2​,λ3​) in C3, there exits a (essentially
unique) trilinear form on C∞(S)×C∞(S)×C∞(S) which is invariant under
πλ1​​⊗πλ2​​⊗πλ3​​. Using
differential operators on the sphere S which are covariant under the
conformal group SO0​(1,n), we construct new invariant trilinear forms
corresponding to singular values of λ. The family of
generic invariant trilinear forms depend meromorphically on the parameter
λ and the new forms are shown to be residues of this
family