Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

Elena Fuchs, Chen Meiri, Peter Sarnak

Type: Article

Publication Date: 2014-09-17

Citations: 35

DOI: https://doi.org/10.4171/jems/471

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.

Locations

Journal of the European Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
Journal of the European Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
Journal of the European Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF

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