有限Chevalley群的Kazhdan-Laumon表示、character层和Lefschetz-Verdeier迹公式的某些推广
Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formula
摘要：
本文研究了有限域上约化群的表示。我们表明，一般这些表示是不可约的，他们的字符是等于由弗罗贝尼乌斯态射的相应的Lusztig的特征层的茎的痕迹得到的功能。这与G.Lusztig的相应结果一起意味着一般的Kazhdan-Laumon表示同构于相应的Deligne-Lusztig表示。在本文的后半部分，我们给出了一个直接的尺规作图法，这个同构，假设某些推广的Lefschetz-Verdier迹公式持有。
英文摘要：
In this paper we investigate the representations of reductive groups over a finite field, introduced in 1987 by D.Kazhdan and G.Laumon. We show that generically these representations are irreducible and that their character is equal to the function obtained by traces of Frobenius morphism on the stalks of the corresponding Lusztig's character sheaf. This, together with the corresponding result by G.Lusztig, implies that generic Kazhdan-Laumon representations are isomorphic to the corresponding Deligne-Lusztig representations. In the second half of the paper we give a direct geometric construction of this isomorphism, assuming that certain generalization of the Lefschetz-Verdier trace formula holds.
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