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arXiv · 2112.07797

Picard modular groups generated by complex reflections

Alice Mark·Julien Paupert·David Polletta
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Abstract

In this short note we use the presentations found in \cite{MP} and \cite{Po} to show that the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ with $d=1,3,7$ (respectively the quaternion hyperbolic lattice ${\rm PSp}(2,1,\mathcal{H})$ with entries in the Hurwitz integer ring $\mathcal{H}$) are generated by complex (resp. quaternionic) reflections, and that the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ with $d=2,11$ have an index 4 subgroup generated by complex reflections.

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Alice Mark, Julien Paupert, David Polletta. 2021-12-14. Picard modular groups generated by complex reflections. https://arxiv.org/abs/2112.07797

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