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