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Real reflections, commutators and cross-ratios in complex hyperbolic space

Abstract : We provide a concrete criterion to determine whether or not two given elements of PU(2,1) can be written as products of real reflections, with one reflection in common. As an application, we show that the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ with $d=1,2,3,7,11$ are generated by real reflections up to index 1, 2, 4 or 8.
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https://hal.archives-ouvertes.fr/hal-00916997
Contributor : Pierre Will Connect in order to contact the contributor
Submitted on : Wednesday, December 11, 2013 - 10:18:39 AM
Last modification on : Tuesday, June 1, 2021 - 9:12:09 PM
Long-term archiving on: : Wednesday, March 12, 2014 - 2:00:09 AM

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  • HAL Id : hal-00916997, version 1
  • ARXIV : 1312.3173

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Julien Paupert, Pierre Will. Real reflections, commutators and cross-ratios in complex hyperbolic space. Groups, Geometry, and Dynamics, European Mathematical Society, 2017, 11 (1), pp.311-352. ⟨hal-00916997⟩

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