The space of monodromy data for the Jimbo–Sakai family of q-difference equations
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 5, pp. 1119-1250.

We formulate a geometric Riemann–Hilbert correspondence that applies to the derivation by Jimbo and Sakai of equation q-PVI from “isomonodromy” conditions. This is a step within work in progress towards the application of q-isomonodromy and q-isoStokes to q-Painlevé.

Nous formulons une correspondance de Riemann–Hilbert géométrique qui s’applique à la dérivation par Jimbo et Sakai de l’équation q-PVI à partir de conditions « d’isomonodromie ». C’est une étape d’un travail en cours en vue de l’application de la q-isomonodromie et des q-isoStokes à q-Painlevé.

Published online:
DOI: 10.5802/afst.1659
Ohyama, Yousuke 1; Ramis, Jean-Pierre 2; Sauloy, Jacques 3

1 Department of Mathematical Sciences, Tokushima University, 2-1 Minamijyousanjima-cho, Tokushima 770-8506, Japan
2 Institut de France (Académie des Sciences) and Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université Paul Sabatier (Toulouse 3), 118 route de Narbonne, 31062 Toulouse CEDEX 9, France
3 Toulouse
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Ohyama, Yousuke; Ramis, Jean-Pierre; Sauloy, Jacques. The space of monodromy data for the Jimbo–Sakai family of $q$-difference equations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 5, pp. 1119-1250. doi : 10.5802/afst.1659. http://www.numdam.org/articles/10.5802/afst.1659/

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