Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions.

DOI10.4171/JEMS/471zbMath1347.20054arXiv1305.0729MaRDI QIDQ466907

Elena Fuchs, Chen Meiri, Peter C. Sarnak

Publication date: 31 October 2014

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0729

zbMATH Keywords

hypergeometric functionshyperbolic groupsCartan involutionshypergeometric monodromy

Mathematics Subject Classification ID

Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Generalized hypergeometric series, ({}_pF_q) (33C20) Hyperbolic groups and nonpositively curved groups (20F67) Other geometric groups, including crystallographic groups (20H15)

Related Items (18)

Integral factorial ratios ⋮ Hypergeometric groups and dynamics on \(K3\) surfaces ⋮ Monodromy of the Multiplicative and the Additive Convolution ⋮ Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy ⋮ Symplectic hypergeometric groups of degree six ⋮ Experimenting with Symplectic Hypergeometric Monodromy Groups ⋮ Arithmeticity of some hypergeometric groups ⋮ A cyclotomic family of thin hypergeometric monodromy groups in \({\mathrm{Sp}}_4({\mathbb{R}})\) ⋮ Commensurability and Arithmetic Equivalence for Orthogonal Hypergeometric Monodromy Groups ⋮ Cones and ping-pong in three dimensions ⋮ Working session: Thin groups and super-approximation. Abstracts from the working session held October 10--15, 2021 (hybrid meeting) ⋮ Arithmeticity of certain symplectic hypergeometric groups ⋮ Non-arithmetic monodromy of higher hypergeometric functions ⋮ Arithmeticity of some hypergeometric monodromy groups in Sp(4) ⋮ Hypergeometric groups of orthogonal type ⋮ Arithmetic hyperbolic reflection groups ⋮ On orthogonal hypergeometric groups of degree five ⋮ Constructing thin subgroups of \(\text{SL}(n + 1, \mathbb{R})\) via bending

Cites Work

• Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros
• Self-correspondences of \(K3\) surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups
• Monodromy for the hypergeometric function \(_ nF_{n-1}\)
• The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces
• A note on optimal unimodular lattices
• \(p\)-adic cycles
• Arithmeticity of certain symplectic hypergeometric groups
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