Arithmeticity of some hypergeometric groups

Arithmeticity of complex hyperbolic triangle groups

Complex hyperbolic triangle groups, originally studied by Mostow in building the first nonarithmetic lattices in PU(2, 1), are a natural generalization of the classical triangle groups. A theorem of Takeuchi states that there are only finitely many Fuchsian triangle groups that determine an arithmetic lattice in PSL2(R), so triangle groups are generically nonarithmetic. We prove similar finiten...

Integrality and arithmeticity of solvable linear groups

Article history: Received 25 October 2013 Accepted 10 March 2014 Available online 11 August 2014

On a Problem concerning Arithmeticity of Discrete Groups Acting

We discuss an open problem on the discreteness of subgroups of (SL2(R)) (n ≥ 2) generated by n linearly independent upper triangular matrices and n linearly independent lower triangular matrices. According to a conjecture by Margulis, only Hilbert modular groups can arise this way. The purpose of this note is to explain how this open problem is related to another conjecture on the orbit behavio...

Rigidity Results for Groups with Radical Cohomology of Finite Groups and Arithmeticity Problems

Symmetry Groups of A n Hypergeometric Series ?

Structures of symmetries of transformations for Holman–Biedenharn–Louck An hypergeometric series: An terminating balanced 4F3 series and An elliptic 10E9 series are discussed. Namely the description of the invariance groups and the classification all of possible transformations for each types of An hypergeometric series are given. Among them, a “periodic” affine Coxeter group which seems to be ...