Abstract:We prove that for extended Dynkin quivers, simple perverse sheaves in Lusztig category are characterized by the nilpotency of their singular support. This proves a conjecture of Lusztig in the case of affine quivers. For cyclic quivers, we prove a similar result for a larger nilpotent variety and a larger class of perverse sheaves. We formulate conjectures concerning similar results for quivers with loops, for which we have to use the appropriate notion of nilpotent variety, due to Bozec, Schiffmann and Vasserot. We prove our conjecture for $g$-loops quivers ($g\geq 2$).

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中文翻译：

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Lusztig 滑轮用于仿射颤动和 𝑔-loop 颤动的微观局部表征

摘要：我们证明了对于扩展的 Dynkin 颤动，Lusztig 范畴的简单反滑轮的特征在于其奇异支撑的幂零性。这证明了 Lusztig 在仿射箭袋的情况下的猜想。对于循环颤动，我们证明了更大的幂零品种和更大类别的反常滑轮的类似结果。由于 Bozec、Schiffmann 和 Vasserot，我们对带有环的箭袋的类似结果提出了猜想，为此我们必须使用适当的幂零变异概念。我们证明了我们对 $g$-loops quivers ($g\geq 2$) 的猜想。

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