Lusztig's canonical quotient and generalized duality
Lusztig's canonical quotient and generalized duality
复制标题
Lusztig 的正则商和广义对偶性
DOI：
10.1006/jabr.2001.8868
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发表时间：
2001
影响因子：
0.9
通讯作者：
E. Sommers
中科院分区：
文献类型：
--
作者：
E. Sommers
摘要 我们给出了 Lusztig 正则商的新表征，该正则商是附加到复半单李代数的每个特殊幂零轨道的有限群。该群在李型有限群的单能表示分类中起着重要作用。我们还定义了对偶图。对于每对幂零轨道和其基本群中的共轭类，该映射在朗兰兹对偶李代数中分配一个幂零轨道。该地图是满射的，与 Lusztig 引入的地图（并由斯帕尔滕斯坦研究）相关。当共轭类微不足道时，我们的对偶图就是斯帕尔滕斯坦、巴巴什和沃根研究的图，它具有一组特殊幂零轨道的图像。
Abstract We give a new characterization of Lusztig's canonical quotient, a finite group attached to each special nilpotent orbit of a complex semisimple Lie algebra. This group plays an important role in the classification of unipotent representations of finite groups of Lie type. We also define a duality map. To each pair of a nilpotent orbit and a conjugacy class in its fundamental group, the map assigns a nilpotent orbit in the Langlands dual Lie algebra. This map is surjective and is related to a map introduced by Lusztig (and studied by Spaltenstein). When the conjugacy class is trivial, our duality map is just the one studied by Spaltenstein and by Barbasch and Vogan which has an image of the set of special nilpotent orbits.