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

Julien Paupert; Pierre Will

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arXiv · 1312.3173

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

Julien Paupert·Pierre Will

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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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Julien Paupert, Pierre Will. 2013-12-11. Real reflections, commutators and cross-ratios in complex hyperbolic space. https://arxiv.org/abs/1312.3173

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