Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type

Details Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type

2007-03-06

arxiv.org/abs/math/0703174v2

Mathematics

Differential Geometry

Scientific paper

Let G be either SU(p,2) with p>=2, Sp(2,R) or SO(p,2) with p>=3. The symmetric spaces associated to these G's are the classical bounded symmetric domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using the correspondence between representations of fundamental groups of K\"{a}hler manifolds and Higgs bundles we study representations of uniform lattices of SU(m,1), m>1, into G. We prove that the Toledo invariant associated to such a representation satisfies a Milnor-Wood type inequality and that in case of equality necessarily G=SU(p,2) with p>=2m and the representation is reductive, faithful, discrete, and stabilizes a copy of complex hyperbolic space (of maximal possible induced holomorphic sectional curvature) holomorphically and totally geodesically embedded in the Hermitian symmetric space SU(p,2)/S(U(p)xU(2)), on which it acts cocompactly.

Affiliated with

Also associated with

No associations

Rating

Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-235236