# Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

Elena Fuchs; Chen Meiri; Peter Sarnak

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 8, page 1617-1671
- ISSN: 1435-9855

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topFuchs, 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 -

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