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Real reflections, commutators and cross-ratios in complex hyperbolic space
Published 11 Dec 2013 in math.GT | (1312.3173v1)
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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