Rigidity, counting and equidistribution of quaternionic Cartan chains
Annales mathématiques Blaise Pascal, Volume 28 (2021) no. 1, pp. 45-69.

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.

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.

Published online:
DOI: 10.5802/ambp.399
Classification: 11E39, 11F06, 11N45, 20G20, 53C17, 53C55
Keywords: counting, equidistribution, Cartan chain, quaternionic Heisenberg group, Cygan distance, sub-Riemannian geometry, quaternionic hyperbolic geometry
Mot clés : comptage, équidistribution, chaîne de Cartan, groupe de Heisenberg quaternionien, distance de Cygan, géométrie sous-riemanienne, géométrie hyperbolique quaternionienne
Jouni Parkkonen 1; Frédéric Paulin 2

1 Department of Mathematics and Statistics P.O. Box 35 40014 University of Jyväskylä FINLAND
2 Laboratoire de mathématique d’Orsay UMR 8628 CNRS Université Paris-Saclay 91405 ORSAY Cedex FRANCE
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jouni Parkkonen; Frédéric Paulin. Rigidity, counting and equidistribution  of quaternionic Cartan chains. Annales mathématiques Blaise Pascal, Volume 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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