Maximal representations, non-Archimedean Siegel spaces, and buildings

Marc Burger, Maria Beatrice Pozzetti
2017 Geometry and Topology  
Let F be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in Sp(2n, F). We show that ultralimits of maximal representations in Sp(2n, R) admit such a framing, and that all maximal framed representations satisfy a suitable generalisation of the classical Collar Lemma. In particular this establishes a Collar Lemma for all maximal representations into Sp(2n, R). We then describe a procedure to get from
more » ... ons in Sp(2n, F) interesting actions on affine buildings, and, in the case of representations admitting a maximal framing, we describe the structure of the elements of the group acting with zero translation length.
doi:10.2140/gt.2017.21.3539 fatcat:nbgcfdkxkfbqnjodmtqnpqjsim