Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

Fuchs, Elena, Meiri, Chen, and Sarnak, Peter. "Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions." Journal of the European Mathematical Society 016.8 (2014): 1617-1671. <http://eudml.org/doc/277402>.

@article{Fuchs2014,
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 $_nF_\{n-1\}$ are thin.},
author = {Fuchs, Elena, Meiri, Chen, Sarnak, Peter},
journal = {Journal of the European Mathematical Society},
keywords = {hypergeometric monodromy; hyperbolic groups; Cartan involutions; hypergeometric monodromy; hyperbolic groups; Cartan involutions},
language = {eng},
number = {8},
pages = {1617-1671},
publisher = {European Mathematical Society Publishing House},
title = {Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions},
url = {http://eudml.org/doc/277402},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Fuchs, Elena
AU - Meiri, Chen
AU - Sarnak, Peter
TI - Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 8
SP - 1617
EP - 1671
AB - 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 $_nF_{n-1}$ are thin.
LA - eng
KW - hypergeometric monodromy; hyperbolic groups; Cartan involutions; hypergeometric monodromy; hyperbolic groups; Cartan involutions
UR - http://eudml.org/doc/277402
ER -