Maximal representations, non-Archimedean Siegel spaces, and buildings

Abstract

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 generalization 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 representations 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.

Locations

• arXiv (Cornell University) - View - PDF
• Warwick Research Archive Portal (University of Warwick) - View - PDF
• Project Euclid (Cornell University) - View - PDF
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• Geometry & Topology - View