Classification of tight homomorphisms

2014/12/19 by Oskar Hamlet, Hamlet, Oskar, Maria Beatrice Pozzetti +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1412.6398

29 pages

arxiv created 2014/12/19 · arxiv updated 2014/12/22

Abstract

A totally geodesic map f:\mathcal X₁→\mathcal X₂ between Hermitian symmetric spaces is tight if its image contains geodesic triangles of maximal area. Tight maps were first introduced in [BIW09], and were classified in [Ham13, Ham14, HO14] in the case of irreducible domain. We complete the classification by analyzing also maps from reducible domains. This has applications to the study of maximal representations and of the Hitchin component for representations in the groups Sp(2n,\mathbb R).

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