Picard modular groups generated by complex reflections

DOI10.1090/conm/783/15735OpenAlexW4323646312MaRDI QIDQ5886551

Alice Mark, Julien Paupert, David Polletta

Publication date: 5 April 2023

Published in: Computational Aspects of Discrete Subgroups of Lie Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.07797

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Uses Software

• Magma
• GitHub

Cites Work

• Arithmeticity of complex hyperbolic triangle groups.
• The geometry of the Gauss-Picard modular group
• Enumeration of the 50 fake projective planes
• Fake projective planes
• On the rigidity of certain fundamental groups, arithmeticity of complex hyperbolic lattices, and the ``fake projective planes
• The Leech lattice and complex hyperbolic reflections
• New complex- and quaternion-hyperbolic reflection groups
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Generalized Picard lattices arising from half-integral conditions
• New nonarithmetic complex hyperbolic lattices. II
• Presentations for the Euclidean Picard modular groups
• Arithmeticity, superrigidity, and totally geodesic submanifolds
• A new nonarithmetic lattice in \(\mathrm{PU}(3,1)\)
• Real reflections, commutators, and cross-ratios in complex hyperbolic space
• Reflective and quasi-reflective Bianchi groups.
• The geometry of the Eisenstein-Picard modular group
• Geometry of quaternionic hyperbolic manifolds
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