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1 IMB - Institut de Mathématiques de Bordeaux 2 Géométrie IECL - Institut Élie Cartan de Lorraine

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

Author: Vincent Koziarz - Julien Maubon -



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