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Cartan decomposition for
$\mathrm {Sp}(1,n)$ and some applications to group dynamics
- Part of
-
- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 28 October 2025, pp. 1-17
-
- Article
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In this article, we present an elementary proof of the Cartan decomposition theorem for the group
$ \mathrm {Sp}(1, n) $. As an application, we determine the largest regular domain for discrete quaternionic hyperbolic groups acting on 
$ \mathbb {HP}^n $. Furthermore, we demonstrate that Bers’ simultaneous uniformization and Köebe’s retrosection theorem fail to hold for higher-dimensional quaternionic Kleinian groups.
