The work of the first author on the moment map for representations of quivers included a classification of the possible dimension vectors of simple modules for deformed preprojective algebras. That classification was later used to solve an additive analogue of the Deligne-Simpson problem. The last step in the proof of the classification involved some general position arguments; here we give a new approach which avoids such arguments.

中文翻译：

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投影前代数简单模块的新方法

第一作者在弯矩表示的矩图上的工作包括对变形的投影前代数的简单模块的可能维数矢量的分类。该分类后来用于解决Deligne-Simpson问题的加法模拟。分类证明的最后一步涉及一些一般的位置论证。在这里，我们给出一种避免这种争论的新方法。