title: On arc coordinates for maximal representations
creator: Magnani, Marta
subject: ddc-510
subject: 510 Mathematics
description: Given a hyperbolic surface with boundary, arc coordinates provide a parametrization of the Teichmüller space. They rely on the choice of a family of arcs which start and end at boundary components and are orthogonal to them. Higher rank Teichmüller theories are a generalization of classical Teichmüller theory and are concerned with the study of representations of the fundamental group of an oriented surface of negative Euler characteristic into simple real Lie groups G of higher rank. It is well known that maximal representations are a higher rank Teichmüller theory for G Hermitian. In this thesis we will discuss how to generalize arc coordinates for maximal representations, focusing on the case where the surface is a pair of pants and G is PSp(4,R). This will be possible by introducing geometric parameters on the space of right-angled hexagons in the Siegel space X, which lead to the visualization of a right-angled hexagon as a polygonal chain inside the hypervolic plane. We discuss geometric properties of reflections in X and introduce the notion of maximal representations of a reflection group W3. We give a parametrization of maximal representations of W3 into PSp(4,R), which allows us to parametrize a subset of maximal and Shilov hyperbolic representations into PSp(4,R).
date: 2024
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/34521/1/On%20arc%20coordinates%20for%20maximal%20representations.pdf
identifier: DOI:10.11588/heidok.00034521
identifier: urn:nbn:de:bsz:16-heidok-345215
identifier:   Magnani, Marta  (2024) On arc coordinates for maximal representations.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/34521/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng