The orbital counting problem for hyperconvex representations
Annales de l'Institut Fourier, Volume 65 (2015) no. 4, pp. 1755-1797.

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.

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.

DOI: 10.5802/aif.2973
Classification: 22E40,  37D20
Keywords: Lie groups, higher rank geometries, Hitchin representations
Sambarino, Andrés 1

1 Université Pierre et Marie Curie Institut de Mathématiques de Jussieu 4 place Jussieu, 75252 Paris Cedex (France)
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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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