A classification of $\mathbb R$-Fuchsian subgroups of Picard modular groups

@article{Parkkonen2015ACO,
  title={A classification of \$\mathbb R\$-Fuchsian subgroups of Picard modular groups},
  author={Jouni Parkkonen and F. Paulin},
  journal={arXiv: Number Theory},
  year={2015}
}
Given an imaginary quadratic extension $K$ of $\mathbb Q$, we give a classification of the maximal nonelementary subgroups of the Picard modular group $\operatorname{PSU}_{1,2}(\mathcal O_K)$ preserving a complex geodesic in the complex hyperbolic plane $\mathbb H^2_\mathbb C$. Complementing work of Holzapfel, Chinburg-Stover and M\"oller-Toledo, we show that these maximal $\mathbb C$-Fuchsian subgroups are arithmetic, arising from a quaternion algebra $\Big(\!\begin{array}{c} D\,,D_K\\\hline… Expand
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