Maximal representations of uniform complex hyperbolic lattices
Langue
en
Article de revue
Ce document a été publié dans
Annals of Mathematics. 2017, vol. 185, n° 2, p. 493-540
Princeton University, Department of Mathematics
Résumé en anglais
Let ρ be a maximal representation of a uniform lattice Γ ⊂ SU(n, 1), n ≥ 2, in a classical Lie group of Hermitian type G. We prove that necessarily G = SU(p, q) with p ≥ qn and there exists a holomorphic or antiholomorphic ...Lire la suite >
Let ρ be a maximal representation of a uniform lattice Γ ⊂ SU(n, 1), n ≥ 2, in a classical Lie group of Hermitian type G. We prove that necessarily G = SU(p, q) with p ≥ qn and there exists a holomorphic or antiholomorphic ρ-equivariant map from the complex hyperbolic n-space to the symmetric space associated to SU(p, q). This map is moreover a totally geodesic homothetic embedding. In particular, up to a representation in a compact subgroup of SU(p, q), the representation ρ extends to a representation of SU(n, 1) in SU(p, q).< Réduire
Mots clés en anglais
Tangents
Mathematical lattices
Lie groups
Curvature
Boson fields
Mathematical vectors
Symmetry
Loci
Nonreductive physicalism
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Groupes fondamentaux, Théorie de Hodge et Motifs - ANR-16-CE40-0011
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