For each lattice complex hyperbolic triangle group, we study the Fuchsian stabilizers of (reprentatives of each group orbit of) mirrors of complex reflections. We give explicit generators for the stabilizers, and compute their signature in the sense of Fuchsian groups. For some groups, we also find explicit pairs of complex lines such that the union of their stabilizers generate the ambient lattice.

中文翻译：

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用于晶格复双曲三角形群的镜面稳定器

对于每个晶格复双曲三角形群，我们研究复反射镜（每组轨道的代表）的福克斯稳定器。我们给出稳定器的显式生成器，并计算它们在 Fuchsian 群意义上的签名。对于某些组，我们还发现了显式的复杂线对，使得它们的稳定剂的结合生成了环境晶格。