Appears in collection : Symmetry in Geometry and Analysis

For three representations of the principal series of the conformal group of the sphere $S^n$, the dimension of the space of continuous trilinear invariant forms on $C^\infty (S^n) \times C^\infty (S^n) \times C^\infty (S^n)$ is determined, and a basis is described. The results are intimately connected with the study of conformally covariant differential and bi-differential operators.