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Maximal representations of uniform complex hyperbolic lattices
Language
en
Article de revue
This item was published in
Annals of Mathematics. 2017, vol. 185, n° 2, p. 493-540
Princeton University, Department of Mathematics
English Abstract
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 ...Read more >
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).Read less <
English Keywords
Tangents
Mathematical lattices
Lie groups
Curvature
Boson fields
Mathematical vectors
Symmetry
Loci
Nonreductive physicalism
ANR Project
Groupes fondamentaux, Théorie de Hodge et Motifs - ANR-16-CE40-0011
Origin
Hal imported