Singular conformally invariant trilinear forms, II The higher multiplicity cases

Abstract

Let $S$ be the sphere of dimension $n-1,n\ge 4$. Let $({\pi }_{\lambda }{)}_{\lambda \in \mathbb{C}}$ be the scalar principle series of representations of the conformal group $S{O}_0(1,n)$, realized on ${\mathcal{C}}^{\infty }(S)$. For $\mathbf{\lambda }=({\lambda }_1,{\lambda }_2,{\lambda }_3)\in {\mathbb{C}}^3$, let $Tri(\mathbf{\lambda })$ be the space of continuous trilinear forms on ${\mathcal{C}}^{\infty }(S)\times {\mathcal{C}}^{\infty }(S)\times {\mathcal{C}}^{\infty }(S)$ which are invariant under ${\pi }_{{\lambda }_1}\otimes {\pi }_{{\lambda }_2}\otimes {\pi }_{{\lambda }_3}$. For each value of $\mathbf{\lambda }$, the dimension of $Tri(\mathbf{\lambda })$ is computed and a basis of $Tri(\mathbf{\lambda })$ is described.

References in corpus (2)

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