The orbital counting problem for hyperconvex representations
[Sur le décompte orbital pour les representations hyperconvexes]
Annales de l'Institut Fourier, Tome 65 (2015) no. 4, pp. 1755-1797.

Nous trouvons un asymptotique pour le comptage orbitale dans l’espace symétrique d’un groupe de Lie connexe, réel-algébrique, semisimple et non-compact G, pour une classe des sous groupes discrets de G qui contient, par exemple, representations d’un groupe de surface dans PSL(2,)×PSL(2,) induites par la choix de deux éléments de l’espace de Teichmüller de la surface et les representations dans la composante de Hitchin de PSL(d,). Nous démontrons aussi, dans ce contexte, une propriété de melange pour le flot des chambres de Weyl.

We give a precise counting result on the symmetric space of a connected noncompact real-algebraic semisimple Lie group G, for a class of discrete subgroups of G that contains, for example, representations of a surface group on PSL(2,)×PSL(2,), induced by choosing two points on the Teichmüller space of the surface and representations on the Hitchin component of PSL(d,). We also prove a mixing property for the Weyl chamber flow in this setting.

DOI : https://doi.org/10.5802/aif.2973
Classification : 22E40,  37D20
Mots 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/}
}
Sambarino, Andrés. The orbital counting problem for hyperconvex representations. Annales de l'Institut Fourier, Tome 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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