Stokes matrices of hypergeometric integrals

Alexey Glutsyuk[1]; Christophe Sabot[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)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 1, page 291-317
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Glutsyuk, Alexey, and Sabot, Christophe. "Stokes matrices of hypergeometric integrals." Annales de l’institut Fourier 60.1 (2010): 291-317. <http://eudml.org/doc/116269>.

@article{Glutsyuk2010,
abstract = {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.},
affiliation = {École normale supérieure de Lyon Unité de Mathématiques pures et appliquées 46 allée d’Italie 69364 Lyon 07 (France); Université de Lyon 1 Institut Camille Jordan 43 bd du 11 nov. 1918 69622 Villeurbanne cedex (France)},
author = {Glutsyuk, Alexey, Sabot, Christophe},
journal = {Annales de l’institut Fourier},
keywords = {Hyperplane arrangement; hypergeometric integrals; linear ordinary differential equation; Stokes matrix; hyperplane arrangement},
language = {eng},
number = {1},
pages = {291-317},
publisher = {Association des Annales de l’institut Fourier},
title = {Stokes matrices of hypergeometric integrals},
url = {http://eudml.org/doc/116269},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Glutsyuk, Alexey
AU - Sabot, Christophe
TI - Stokes matrices of hypergeometric integrals
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 1
SP - 291
EP - 317
AB - 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.
LA - eng
KW - Hyperplane arrangement; hypergeometric integrals; linear ordinary differential equation; Stokes matrix; hyperplane arrangement
UR - http://eudml.org/doc/116269
ER -

References

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  10. Jean-Pierre Ramis, Confluence et résurgence, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (1989), 703-716 Zbl0722.33003MR1039492
  11. Christophe Sabot, Markov chains in a Dirichlet environment and hypergeometric integrals, C. R. Math. Acad. Sci. Paris 342 (2006), 57-62 Zbl1087.60078MR2193397
  12. A. N. Varchenko, The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. I, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), 1206-1235, 1337 Zbl0695.33004MR1039962
  13. A. N. Varchenko, The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. II, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), 146-158, 222 Zbl0699.33004MR1044052
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