New complex- and quaternion-hyperbolic reflection groups

DOI10.1215/S0012-7094-00-10326-2zbMath0962.22007arXivmath/9907193OpenAlexW2593661150MaRDI QIDQ1572891

Daniel Allcock

Publication date: 7 June 2001

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9907193

zbMATH Keywords

hyperbolic spacessymmetry groupsquaternionsreflection groupsLorentzian latticecomplex cubic surfaces

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Discrete subgroups of Lie groups (22E40) Other groups and their modular and automorphic forms (several variables) (11F55) Differential geometry of symmetric spaces (53C35) Bilinear and Hermitian forms (11E39)

Related Items

The complex hyperbolic geometry of the moduli space of cubic surfaces, Picard modular groups generated by complex reflections, The number of convex tilings of the sphere by triangles, squares, or hexagons, Counting and equidistribution in quaternionic Heisenberg groups, The complex Lorentzian Leech lattice and the bimonster, Reflection group of the quaternionic Lorentzian Leech lattice, Periods of cubic surfaces with the automorphism group of order \(54\), Quaternionic hyperbolic lattices of minimal covolume, Reflective obstructions of unitary modular varieties, Presentations for cusped arithmetic hyperbolic lattices, Hyperbolic geometry and moduli of real curves of genus three, Arithmetic hyperbolic reflection groups, Reflection groups on the octave hyperbolic plane, Classification of quaternionic hyperbolic isometries, A new complex reflection group in \(PU(9,1)\) and the Barnes-Wall lattice, Integral binary Hamiltonian forms and their waterworlds, Theta constants associated with the cyclic triple coverings of the complex projective line branching at six points

Cites Work

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• Arithmetic subgroups of algebraic groups
• Lattices like the Leech lattice
• Automorphism groups of Lorentzian lattices
• On a remarkable class of polyhedra in complex hyperbolic space
• Laminated lattices
• Some lattices over \(Q(\sqrt{-3})^*\)
• Reflection groups on the octave hyperbolic plane
• The Leech lattice and complex hyperbolic reflections
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Generalized Picard lattices arising from half-integral conditions
• The automorphism group of the 26-dimensional even unimodular Lorentzian lattice
• Neighborhood in the sense of Kneser for quaternionic lattices
• On unimodular integral quadratic forms
• The Coxeter–Todd lattice, the Mitchell group, and related sphere packings
• On Discontinuous Action of Monodromy Groups on the Complex n-Ball
• The covering radius of the Leech lattice
• A complex hyperbolic structure for moduli of cubic surfaces
• Classification of Two Genera of 32-Dimensional Lattices of Rank 8 over the Hurwitz Order
• ON GROUPS OF UNIT ELEMENTS OF CERTAIN QUADRATIC FORMS