### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 069, 8 pages      arXiv:1706.05155      https://doi.org/10.3842/SIGMA.2017.069
Contribution to the Special Issue on Elliptic Hypergeometric Functions and Their Applications

### An Elliptic Garnier System from Interpolation

Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan

Received June 20, 2017, in final form August 30, 2017; Published online September 02, 2017

Abstract
Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extension of the elliptic Painlevé equation.

Key words: elliptic difference; isomonodromic systems; Lax form; interpolation problem.

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