We give a precise counting result on the symmetric space of a connected noncompact real-algebraic semisimple Lie group for a class of discrete subgroups of that contains, for example, representations of a surface group on induced by choosing two points on the Teichmüller space of the surface and representations on the Hitchin component of We also prove a mixing property for the Weyl chamber flow in this setting.
Nous trouvons un asymptotique pour le comptage orbitale dans l’espace symétrique d’un groupe de Lie connexe, réel-algébrique, semisimple et non-compact pour une classe des sous groupes discrets de qui contient, par exemple, representations d’un groupe de surface dans induites par la choix de deux éléments de l’espace de Teichmüller de la surface et les representations dans la composante de Hitchin de Nous démontrons aussi, dans ce contexte, une propriété de melange pour le flot des chambres de Weyl.
Keywords: Lie groups, higher rank geometries, Hitchin representations
Mot clés : groupes de Lie, géométrie en rang supérieur, representations de Hitchin
@article{AIF_2015__65_4_1755_0, author = {Sambarino, Andr\'es}, title = {The orbital counting problem for hyperconvex representations}, journal = {Annales de l'Institut Fourier}, pages = {1755--1797}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {4}, year = {2015}, doi = {10.5802/aif.2973}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2973/} }
TY - JOUR AU - Sambarino, Andrés TI - The orbital counting problem for hyperconvex representations JO - Annales de l'Institut Fourier PY - 2015 SP - 1755 EP - 1797 VL - 65 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2973/ DO - 10.5802/aif.2973 LA - en ID - AIF_2015__65_4_1755_0 ER -
%0 Journal Article %A Sambarino, Andrés %T The orbital counting problem for hyperconvex representations %J Annales de l'Institut Fourier %D 2015 %P 1755-1797 %V 65 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2973/ %R 10.5802/aif.2973 %G en %F AIF_2015__65_4_1755_0
Sambarino, Andrés. The orbital counting problem for hyperconvex representations. Annales de l'Institut Fourier, Volume 65 (2015) no. 4, pp. 1755-1797. doi : 10.5802/aif.2973. http://archive.numdam.org/articles/10.5802/aif.2973/
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