Real reflections, commutators and cross-ratios in complex hyperbolic space

2013/12/11 by Julien Paupert, Paupert, Julien, Pierre Will +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1312.3173

Abstract

We provide a concrete criterion to determine whether or not two given elements of PU(2,1) can be written as products of real reflections, with one reflection in common. As an application, we show that the Picard modular groups \rm PU(2,1,O_d) with d=1,2,3,7,11 are generated by real reflections up to index 1, 2, 4 or 8.

Cited by

• Strongly Doubly Reversible Pairs in Quaternionic Unitary Group of Signature (n,1)

Related

• Picard modular groups generated by complex reflections
• On the geometry of a Picard modular group
• Reflections, bendings, and pentagons
• Finite complex reflection arrangements are K(pi,1)
• Finite complex reflection arrangements are K(pi,1)