Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

Elena Fuchs, Chen Meiri, Peter Sarnak

Research output: Contribution to journalArticlepeer-review


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 nFn-1are thin.

Original languageEnglish (US)
Pages (from-to)1617-1671
Number of pages55
JournalJournal of the European Mathematical Society
Issue number8
StatePublished - 2014


  • Cartan involutions
  • Hyperbolic groups
  • Hypergeometric monodromy

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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