Stokes matrices of hypergeometric integrals
Annales de l'Institut Fourier, Volume 60 (2010) no. 1, pp. 291-317.

In this work we compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. This generalizes the computation done by J.-P. Ramis for confluent hypergeometric functions, which correspond to the arrangement of two points on the line. The proof is based on an explicit description of a base of canonical solutions as integrals on the cones of the arrangement, and combinatorial relations between integrals on cones and on domains.

Dans cet article, nous calculons les matrices de Stokes de l’équation différentielle ordinaire satisfaites par les intégrales hypergéométriques, associées à un arrangement d’hyperplans en position générique. Cela généralise le calcul fait par J.-P. Ramis pour les fonctions hypergéométriques confluentes, qui correspondent à l’arrangement de deux points sur une droite. La démonstration est basée sur une description explicite d’une base de solutions canoniques comme intégrales sur les cônes de l’arrangement et les relations combinatoires entre les intégrales sur cônes et sur domaines.

DOI: 10.5802/aif.2523
Classification: 34M40, 52C35, 33C60
Keywords: Hyperplane arrangement, hypergeometric integrals, linear ordinary differential equation, Stokes matrix
Mot clés : arrangement d’hyperplans, intégrales hypergéométriques, équation différentielle ordinaire, matrice de Stokes
Glutsyuk, Alexey 1; Sabot, Christophe 2

1 École normale supérieure de Lyon Unité de Mathématiques pures et appliquées 46 allée d’Italie 69364 Lyon 07 (France)
2 Université de Lyon 1 Institut Camille Jordan 43 bd du 11 nov. 1918 69622 Villeurbanne cedex (France)
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Glutsyuk, Alexey; Sabot, Christophe. Stokes matrices of hypergeometric integrals. Annales de l'Institut Fourier, Volume 60 (2010) no. 1, pp. 291-317. doi : 10.5802/aif.2523. https://aif.centre-mersenne.org/articles/10.5802/aif.2523/

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