Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions
Group Theory
2013-08-13 v2 Number Theory
Abstract
We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature (n-1,1) is "thin", namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg's theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for n_F_(n-1) are thin.
Keywords
Cite
@article{arxiv.1305.0729,
title = {Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions},
author = {Elena Fuchs and Chen Meiri and Peter Sarnak},
journal= {arXiv preprint arXiv:1305.0729},
year = {2013}
}
Comments
49 pages, 16 figures