Maximal representations of complex hyperbolic lattices
Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015
Location: SLMath: Eisenbud Auditorium
lattice of isometries
projective unitary representations
discrete group actions
rigidity results
complex geometry
non-definite Hermitian forms
14216
There are natural incidence structures on the boundary of the complex hyperbolic space and on some suitable boundary S associated to the group PU(m,n). Such structures have striking rigidity properties: I will prove that a (measurable) map from the boundary of the complex hyperbolic space to S that preserves these incidence structures needs to be algebraic. This implies that, if G is a lattice in SU(1,p) and n is greater than m, there exist Zariski dense maximal representations of G in SU(m,n) only if (m,n) is equal to (1,p). In particular the restriction to G of the diagonal embedding of SU(1,p) in SU(m,pm+k) is locally rigid.
Pozzetti.Notes
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14216
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