Mirror stabilizers for lattice complex hyperbolic triangle groups

Abstract

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.