Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions
By E. Fuchs, C. Meiri, Peter Sarnak. 2013
47 citations recorded by the source corpus.
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 n_F_(n-1) are thin.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a0e4e13d5f994142ece48a121dafef5d915b41b7
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In Geometry and Topology
- Christopher Brav
- Hugh Thomas
- I. Reiten
- Osamu Iyama
- B. Keller
- Lingyan Guo
- Ralf Schiffler
- Gustavo Jasso
In Mathematical Physics
Citations in the corpus
- Thin monodromy in Sp(4) (2012, methodology): “sed by Griths-Schmid ([7]). Non-arithmetic or ‘thin’ examples were given by Deligne-Mostow ([4])and Nori ([11]), and more general examples in a similar spirit will be provided by Fuchs-Meiri-Sarnak ([6]). In all these examples, however, the Zariski closure of the monodromy group has real rank 1 or i”