群紧化的半稳定轨迹上的Character层
Character sheaves on the semi-stable locus of a group compactification
摘要：
研究伴随群上特征标层到其奇妙紧化的半稳定轨迹的中间扩张。我们表明，中间扩展可以描述一个直接的图像建设。因此，我们证明了紧化的特征层对半稳定轨迹内的边界片的“普通”限制是半单反常层的移位，并且与Lusztig的限制函子（从约化群上的特征层到Levi子群上的特征层的直和）密切相关。我们还给出了有限Lie型群的不可约特征标的半稳定轨迹内的边值的一个（几何）公式，它部分地回答了Springer \cite{Sp2}的一个问题.这个公式适用于Steinberg字符和来自通用字符层的字符。最后，我们在奇妙紧化的半稳定轨迹内验证了Lusztig猜想\cite [12.6]{L3}.
英文摘要：
We study the intermediate extension of the character sheaves on an adjoint group to the semi-stable locus of its wonderful compactification. We show that the intermediate extension can be described by a direct image construction. As a consequence, we show that the ``ordinary'' restriction of a character sheaf on the compactification to a boundary piece inside the semi-stable locus is a shift of semisimple perverse sheaf and is closely related to Lusztig's restriction functor (from a character sheaf on a reductive group to a direct sum of character sheaves on a Levi subgroup). We also provide a (conjectural) formula for the boundary values inside the semi-stable locus of an irreducible character of a finite group of Lie type, which gives a partial answer to a question of Springer \cite{Sp2}. This formula holds for Steinberg character and characters coming from generic character sheaves. In the end, we verify Lusztig's conjecture \cite[12.6]{L3} inside the semi-stable locus of the wonderful compactification.
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