Dans ce papier, nous montrons un analogue d’un théorème de Cartan, disant que les transformations du bord des espaces hyperboliques quaternioniens qui préservent les chaînes sont des transformations projectives. Nous donnons un résultat de comptage et d’équidistribution pour les orbites de chaînes arithmétiques dans le groupe de Heisenberg quaternionien.
In this paper, we prove an analog of Cartan’s theorem, saying that the chain-preserving transformations of the boundary of the quaternionic hyperbolic spaces are projective transformations. We give a counting and equidistribution result for the orbits of arithmetic chains in the quaternionic Heisenberg group.
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@article{AMBP_2021__28_1_45_0,
author = {Jouni Parkkonen and Fr\'ed\'eric Paulin},
title = {Rigidity, counting and equidistribution of quaternionic {Cartan} chains},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {45--69},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {28},
number = {1},
year = {2021},
doi = {10.5802/ambp.399},
language = {en},
url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.399/}
}
TY - JOUR AU - Jouni Parkkonen AU - Frédéric Paulin TI - Rigidity, counting and equidistribution of quaternionic Cartan chains JO - Annales mathématiques Blaise Pascal PY - 2021 SP - 45 EP - 69 VL - 28 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.399/ DO - 10.5802/ambp.399 LA - en ID - AMBP_2021__28_1_45_0 ER -
%0 Journal Article %A Jouni Parkkonen %A Frédéric Paulin %T Rigidity, counting and equidistribution of quaternionic Cartan chains %J Annales mathématiques Blaise Pascal %D 2021 %P 45-69 %V 28 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.399/ %R 10.5802/ambp.399 %G en %F AMBP_2021__28_1_45_0
Jouni Parkkonen; Frédéric Paulin. Rigidity, counting and equidistribution of quaternionic Cartan chains. Annales mathématiques Blaise Pascal, Tome 28 (2021) no. 1, pp. 45-69. doi : 10.5802/ambp.399. https://ambp.centre-mersenne.org/articles/10.5802/ambp.399/
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