Let G be a connected reductive algebraic group over an algebraically closed field k . We consider the strata in G defined by Lusztig as fibers of a map given in terms of truncated induction of Springer representations. We elaborate on the existing proof of the following two results in order to show that it extends to arbitrary characteristic: Lusztig’s strata are locally closed and the irreducible components of a stratum X are those sheets for the G -action on itself that are contained in X .

中文翻译：

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Lusztig 的地层局部封闭

令 G 是代数闭域 k 上的连通还原代数群。我们将 Lusztig 定义的 G 中的层视为根据 Springer 表示的截断归纳给出的地图的纤维。我们详细阐述了以下两个结果的现有证明，以表明它可以扩展到任意特征：Lusztig 的层是局部封闭的，层 X 的不可约分量是包含在 X 中的那些对自身的 G 作用的表.