Deformations of maximal representations in Sp(4,R)
Steven B. Bradlow (University of Illinois), Oscar Garcia-Prada (CSIC,, Madrid), Peter B. Gothen (Universidade do Porto)
TL;DR
This paper investigates the deformation space of maximal representations of surface groups into Sp(4,R) using Higgs bundle techniques, focusing on when such representations can be deformed to factor through proper subgroups.
Contribution
It provides a characterization of deformations of maximal Sp(4,R)-representations and identifies conditions under which they factor through proper reductive subgroups.
Findings
Characterization of deformation conditions for maximal representations
Identification of proper reductive subgroups relevant to deformations
Application of Higgs bundle methods to representation theory
Abstract
We use Higgs bundles to answer the following question: When can a maximal Sp(4,R)-representation of a surface group be deformed to a representation which factors through a proper reductive subgroup of Sp(4,R)?
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