Geodesic
Maximal representations of uniform complex hyperbolic lattices
Vincent Koziarz1 ; Julien Maubon2
1 Univ. Bordeaux, IMB, CNRS, UMR 5251, F-33400 Talence, France
2 Université de Lorraine, CNRS, Institut Élie Cartan de Lorraine, UMR 7502, Vandœuvre-lès-Nancy, F-54506, France
Annals of mathematics, Tome 185 (2017) no. 2, pp. 493-540.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $\rho$ be a maximal representation of a uniform lattice $\Gamma\subset\mathrm{SU}(n,1)$, $n\geq 2$, in a classical Lie group of Hermitian type $G$. We prove that necessarily $G=\mathrm{SU}(p,q)$ with $p\geq qn$ and there exists a holomorphic or antiholomorphic $\rho$-equivariant map from the complex hyperbolic $n$-space to the symmetric space associated to $\mathrm{SU}(p,q)$. This map is moreover a totally geodesic homothetic embedding. In particular, up to a representation in a compact subgroup of $\mathrm{SU}(p,q)$, the representation $\rho$ extends to a representation of $\mathrm{SU}(n,1)$ in $\mathrm{SU}(p,q)$.
DOI : 10.4007/annals.2017.185.2.3

Vincent Koziarz 1 ; Julien Maubon 2

1 Univ. Bordeaux, IMB, CNRS, UMR 5251, F-33400 Talence, France
2 Université de Lorraine, CNRS, Institut Élie Cartan de Lorraine, UMR 7502, Vandœuvre-lès-Nancy, F-54506, France 
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Vincent Koziarz; Julien Maubon. Maximal representations of uniform complex hyperbolic lattices. Annals of mathematics, Tome 185 (2017) no. 2, pp. 493-540. doi : 10.4007/annals.2017.185.2.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.2.3/

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