Singular conformally invariant trilinear forms, I Multiplicity one results

Abstract

A normalized holomorphic family (depending on $\mathbf{\lambda }\in {\mathbb{C}}^3$) of conformally invariant trilinear forms on the sphere is studied. Its zero set $Z$ is described. For $\mathbf{\lambda }\notin Z$, the multiplicity of the space of conformally invariant trilinear forms is shown to be 1, except perhaps for a denumerable subset.

This second version gives a positive answer to the conjecture stated in the first version

References in corpus (3)

• Symmetry breaking for representations of rank one orthogonal groups
• Symmetry breaking for representations of rank one orthogonal groups II
• Rankin-Cohen brackets for orthogonal Lie algebras and bilinear conformally invariant differential operators