Maximal representations of uniform complex hyperbolic lattices

• 成果类型: Article
• 署名作者: Koziarz, Vincent; Maubon, Julien
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.185.2.3
• 发表日期: 2017
• 页码: 493-540
• 关键词: surface group-representations; HARMONIC MAPS; deformation rigidity; kahler-manifolds; symmetric-spaces; vector-bundles; Simple proof; geometry; THEOREM; conjecture

摘要

Let rho be a maximal representation of a uniform lattice Gamma subset of 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 rho-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 p extends to a representation of SU(n, 1) in SU(p, q).