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Conformally invariant trilinear forms on the sphere

Jean-Louis Clerc, Bent Ørsted (2011)

Annales de l’institut Fourier

To each complex number λ is associated a representation π λ of the conformal group S O 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 π λ 1 π λ 2 π λ 3 . The trilinear form, first defined for ( λ 1 , λ 2 , λ 3 ) in an open set of 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.

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