JournalsjemsVol. 16, No. 8pp. 1617–1671

Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

  • Elena Fuchs

    University of Illinois, Urbana, USA
  • Chen Meiri

    University of Chicago, USA
  • Peter Sarnak

    Princeton University, United States
Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions cover
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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 (n1,1)(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 nFn1_nF_{n-1} are thin.

Cite this article

Elena Fuchs, Chen Meiri, Peter Sarnak, Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions. J. Eur. Math. Soc. 16 (2014), no. 8, pp. 1617–1671

DOI 10.4171/JEMS/471