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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
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: |
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| 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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