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).
Pozzetti, M.B. (2015). Maximal representations of complex hyperbolic lattices into SU(m,n). GEOMETRIC AND FUNCTIONAL ANALYSIS, 25(4), 1290-1332 [10.1007/s00039-015-0338-3].
Maximal representations of complex hyperbolic lattices into SU(m,n)
Pozzetti M. B.
2015
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
