# An Elliptic Garnier System from Interpolation

## TL;DR

This paper introduces a new class of elliptic difference systems derived from interpolation problems, extending the elliptic Painlevé equation to multiple variables, with associated Lax forms.

## Contribution

It develops a multivariate extension of the elliptic Painlevé equation from interpolation problems, including the derivation of their Lax forms.

## Key findings

- Derived elliptic difference isomonodromic systems from interpolation.
- Extended elliptic Painlevé equation to multivariate case.
- Established Lax forms for the new systems.

## 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 Painlev\'e equation.