Conformally invariant trilinear forms on the sphere

Details Conformally invariant trilinear forms on the sphere Conformally invariant trilinear forms on the sphere

2010-01-16

arxiv.org/abs/1001.2851v1

Mathematics

Representation Theory

Scientific paper

To each complex number $\lambda$ is associated a representation $\pi_\lambda$ of the conformal group $SO_0(1,n)$ on $\mathcal C^\infty(S^{n-1})$ (spherical principal series). For three values $\lambda_1,\lambda_2,\lambda_3$, we construct a trilinear form on $\mathcal C^\infty(S^{n-1})\times\mathcal C^\infty(S^{n-1})\times \mathcal C^\infty(S^{n-1})$, which is invariant by $\pi_{\lambda_1}\otimes \pi_{\lambda_2}\otimes \pi_{\lambda_3}$. The trilinear form, first defined for $(\lambda_1, \lambda_2,\lambda_3)$ in an open set of $\mathbb C^3$ 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.

Affiliated with

Also associated with

No associations

Rating

Conformally invariant trilinear forms on the sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Conformally invariant trilinear forms on the sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conformally invariant trilinear forms on the sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-88547