We introduce the notion of minimal reduction type of an affine Springer fiber, and use it to define a map from the set of conjugacy classes in the Weyl group to the set of nilpotent orbits. We show that this map is the same as the one defined by Lusztig in Lfromto, (2011) and that the Kazhdan–Lusztig map in Kazhdan and Lusztig, (1998) is a section of our map. This settles several conjectures in the literature. For classical groups, we prove more refined results by introducing and studying the “skeleta” of affine Springer fibers.

中文翻译：

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最小归约类型和 Kazhdan-Lusztig 映射

我们引入了仿射 Springer 纤维的最小归约类型的概念，并使用它来定义从 Weyl 群中的一组共轭类到一组幂零轨道的映射。我们表明该地图与 Lusztig 在 Lfromto (2011) 中定义的地图相同，并且 Kazhdan 和 Lusztig (1998) 中的 Kazhdan-Lusztig 地图是我们地图的一部分。这解决了文献中的几个猜想。对于经典群，我们通过引入和研究仿射 Springer 纤维的“骨架”证明了更精细的结果。