Conformally invariant trilinear forms on the sphere

@article{Clerc2011,
abstract = {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.},
affiliation = {Université Henri Poincaré (Nancy 1) Institut Élie Cartan 54506 Vandoeuvre-lès-Nancy (France); Matematisk Institut Byg. 430, Ny Munkegade 8000 Aarhus C (Denmark)},
author = {Clerc, Jean-Louis, Ørsted, Bent},
journal = {Annales de l’institut Fourier},
keywords = {Trilinear invariant forms; conformal group; meromorphic continuation; trilinear invariant forms},
language = {eng},
number = {5},
pages = {1807-1838},
publisher = {Association des Annales de l’institut Fourier},
title = {Conformally invariant trilinear forms on the sphere},
url = {http://eudml.org/doc/219713},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Clerc, Jean-Louis
AU - Ørsted, Bent
TI - Conformally invariant trilinear forms on the sphere
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 5
SP - 1807
EP - 1838
AB - 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.
LA - eng
KW - Trilinear invariant forms; conformal group; meromorphic continuation; trilinear invariant forms
UR - http://eudml.org/doc/219713
ER -