To each complex number is associated a representation of the conformal group on (spherical principal series). For three values , we construct a trilinear form on , which is invariant by . The trilinear form, first defined for in an open set of 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.
À chaque nombre complexe est associée une représentation du groupe conforme sur (série principale sphérique). Pour chaque triplet , nous construisons une forme trilinéaire sur qui est invariante par . La forme trilinéaire, d’abord définie dans un ouvert de est étendue méromorphiquement, avec des pôles simples en une famille explicite de plans de . Pour les valeurs génériques des paramètres, nous démontrons l’unicité d’une telle forme trilinéaire invariante.
Keywords: Trilinear invariant forms, conformal group, meromorphic continuation
Mot clés : formes trilinéaires invariantes, groupe conforme, prolongement méromorphe
@article{AIF_2011__61_5_1807_0, author = {Clerc, Jean-Louis and {\O}rsted, Bent}, title = {Conformally invariant trilinear forms on the sphere}, journal = {Annales de l'Institut Fourier}, pages = {1807--1838}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {5}, year = {2011}, doi = {10.5802/aif.2659}, zbl = {1252.22008}, mrnumber = {2961841}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2659/} }
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 SP - 1807 EP - 1838 VL - 61 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2659/ DO - 10.5802/aif.2659 LA - en ID - AIF_2011__61_5_1807_0 ER -
%0 Journal Article %A Clerc, Jean-Louis %A Ørsted, Bent %T Conformally invariant trilinear forms on the sphere %J Annales de l'Institut Fourier %D 2011 %P 1807-1838 %V 61 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2659/ %R 10.5802/aif.2659 %G en %F AIF_2011__61_5_1807_0
Clerc, Jean-Louis; Ørsted, Bent. Conformally invariant trilinear forms on the sphere. Annales de l'Institut Fourier, Volume 61 (2011) no. 5, pp. 1807-1838. doi : 10.5802/aif.2659. http://www.numdam.org/articles/10.5802/aif.2659/
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