[Matrices de Stokes d’intégrales hypergéométriques]
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.
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.
Keywords: Hyperplane arrangement, hypergeometric integrals, linear ordinary differential equation, Stokes matrix
Mot clés : arrangement d’hyperplans, intégrales hypergéométriques, équation différentielle ordinaire, matrice de Stokes
@article{AIF_2010__60_1_291_0,
author = {Glutsyuk, Alexey and Sabot, Christophe},
title = {Stokes matrices of hypergeometric integrals},
journal = {Annales de l'Institut Fourier},
pages = {291--317},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {60},
number = {1},
year = {2010},
doi = {10.5802/aif.2523},
zbl = {1201.34140},
mrnumber = {2664316},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2523/}
}
TY - JOUR AU - Glutsyuk, Alexey AU - Sabot, Christophe TI - Stokes matrices of hypergeometric integrals JO - Annales de l'Institut Fourier PY - 2010 SP - 291 EP - 317 VL - 60 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2523/ DO - 10.5802/aif.2523 LA - en ID - AIF_2010__60_1_291_0 ER -
%0 Journal Article %A Glutsyuk, Alexey %A Sabot, Christophe %T Stokes matrices of hypergeometric integrals %J Annales de l'Institut Fourier %D 2010 %P 291-317 %V 60 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2523/ %R 10.5802/aif.2523 %G en %F AIF_2010__60_1_291_0
Glutsyuk, Alexey; Sabot, Christophe. Stokes matrices of hypergeometric integrals. Annales de l'Institut Fourier, Tome 60 (2010) no. 1, pp. 291-317. doi : 10.5802/aif.2523. http://www.numdam.org/articles/10.5802/aif.2523/
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