CONFORMALLY INVARIANT TRILINEAR FORMS ON THE SPHERE

摘要

To each complex number λ is associated a representation π_λ of the conformal group SO_0(1, n) on C~∞(S~(n-1)) (spherical principal series). For three values λ_1, λ_2, λ_3, we construct a trilinear form on C~∞(S~(n-1)) × C~∞ (S~(n-1)) × C~∞(S~(n-1)), which is invariant by πλ_1×π_λ_2 × πλ_3. The trilinear form, first defined for (λ_1, λ_2, λ_3) in an open set of C~3 is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms.