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- W2614151001 abstract "We complete the classification of maximal representations of uniform complexhyperbolic lattices in Hermitian Lie groups by dealing with the exceptionalgroups ${rm E}_6$ and ${rm E}_7$. We prove that if $rho$ is a maximalrepresentation of a uniform complex hyperbolic lattice $Gammasubset{rmSU}(1,n)$, $n>1$, in an exceptional Hermitian group $G$, then $n=2$ and $G={rmE}_6$, and we describe completely the representation $rho$. The case ofclassical Hermitian target groups was treated by Vincent Koziarz and the secondnamed author (arxiv:1506.07274). However we do not focus immediately on theexceptional cases and instead we provide a more unified perspective, asindependent as possible of the classification of the simple Hermitian Liegroups. This relies on the study of the cominuscule representation of thecomplexification of the target group. As a by product of our methods, when thetarget Hermitian group $G$ has tube type, we obtain an inequality on the Toledoinvariant of the representation $rho:Gammarightarrow G$ which is strongerthan the Milnor-Wood inequality (thereby excluding maximal representations insuch groups)." @default.
- W2614151001 created "2017-05-26" @default.
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- W2614151001 date "2017-03-24" @default.
- W2614151001 modified "2023-09-27" @default.
- W2614151001 title "Maximal representations of uniform complex hyperbolic lattices in exceptional Hermitian Lie groups" @default.
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