Maximal representations of complex hyperbolic lattices in SU(m,n)

2014/07/15 by Maria Beatrice Pozzetti, Pozzetti, Maria Beatrice
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #math.GR #math.MG

paper · pdf · doi:10.48550/arxiv.1407.3903

41 pages, 2 figures, accepted for pubblication in GAFA

arxiv created 2015/05/26 · arxiv updated 2015/05/28

Abstract

Let Γ denote a lattice in SU(1,p), with p greater than 1. We show that there exists no Zariski dense maximal representation with target SU(m,n) if n>m>1. The proof is geometric and is based on the study of the rigidity properties of the geometry whose points are isotropic m-subspaces of a complex vector space V endowed with a Hermitian metric h of signature (m,n) and whose lines correspond to the 2m dimensional subspaces of V on which the restriction of h has signature (m,m).

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