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Maximal representations of complex hyperbolic lattices

Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015

April 13, 2015 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Maria Beatrice Pozzetti (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath); Università di Bologna)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • lattice of isometries

  • projective unitary representations

  • discrete group actions

  • rigidity results

  • complex geometry

  • non-definite Hermitian forms

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14216
Abstract

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.



 
Supplements
23389?type=thumb Pozzetti.Notes 518 KB application/pdf Download
Video/Audio Files

14216

H.264 Video 14216.mp4 343 MB video/mp4 rtsp://videos.msri.org/14216/14216.mp4 Download
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