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Maximal representations, non Archimedean Siegel spaces, and buildings

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Pozzetti, Maria B. and Burger, Marc (2017) Maximal representations, non Archimedean Siegel spaces, and buildings. Geometry and Topology, 21 (6). pp. 3539-3599. doi:10.2140/gt.2017.21.3539 ISSN 1465-3060.

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Official URL: http://doi.org/10.2140/gt.2017.21.3539

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Abstract

Let FF 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)Sp(2n,F). We show that ultralimits of maximal representations in Sp(2n,R)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)Sp(2n,R). We then describe a procedure to get from representations in Sp(2n,F)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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Representations of groups., Geometry, Differential., Lie groups., Riemann surfaces., Geometry.
Journal or Publication Title: Geometry and Topology
Publisher: Geometry & Topology Publications
ISSN: 1465-3060
Official Date: 31 August 2017
Dates:
DateEvent
31 August 2017Published
19 January 2017Accepted
Volume: 21
Number: 6
Page Range: pp. 3539-3599
DOI: 10.2140/gt.2017.21.3539
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 3 March 2017
Date of first compliant Open Access: 27 September 2017

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