We prove that algebraic solutions of Garnier systems in the irregular case are of two types. The classical ones come from isomonodromic deformations of linear equations with diagonal or dihedral differential Galois group; we give a complete list in the rank N = 2 case (two indeterminates).The pull-back ones come from deformations of coverings over a fixed degenerate hypergeometric equation; we provide a complete list when the differential Galois group is SL 2 (C). By the way, we have a complete list of algebraic solutions for the rank N = 2 irregular Garnier systems.

中文翻译：

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不规则卡尼尔系统代数解的分类

我们证明了不规则情况下 Garnier 系统的代数解有两种类型。经典的来自于对角或二面体微分伽罗瓦群的线性方程的等单向变形；我们在等级 N = 2 的情况下（两个不确定）给出了一个完整列表。回拉来自固定退化超几何方程上的覆盖物变形；当微分伽罗瓦群为 SL 2 (C) 时，我们提供了一个完整的列表。顺便说一下，我们有一个完整的 N = 2 阶不规则 Garnier 系统的代数解列表。