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We study a class of three-point functions on the de Sitter universe and onthe asymptotic cone. A blending of geometrical ideas and analytic methods isused to compute some remarkable integrals, on the basis of a generalizedstar-triangle identity living on the cone and on the complex de Sittermanifold. We discuss an application of the general results to the study of thestability of scalar particles on the Sitter universe.

Triangular invariants, three-point functions and particle stability on the de Sitter universe