关于定义特征的等变双射
On equivariant bijections relative to the defining characteristic
摘要：
本文是对Isaacs，Malle和Navarro提出的证明有限群的表示论中McKay猜想的一般程序的贡献。我们发展了新的方法来处理单群的李型在定义特征的情况下。利用基于中心不连通的连通约化群的表示论的一般性论证，证明了当单群的Schur乘子为2阶时，归纳McKay条件成立.因此，单群\Orth_{2m+1}（p^n）和PSp_{2m}（p^n）对p>2是“好的”，而单群E_7（p^n）对p>3是“好的”，这是Isaacs、Malle和Navarro的观点。我们还描述了对角自同构和域自同构在半单和正则特征标上的作用。
英文摘要：
This paper is a contribution to the general program introduced by Isaacs, Malle and Navarro to prove the McKay conjecture in the representation theory of finite groups. We develop new methods for dealing with simple groups of Lie type in the defining characteristic case. Using a general argument based on the representation theory of connected reductive groups with disconnected center, we show that the inductive McKay condition holds if the Schur multiplier of the simple group has order 2. As a consequence, the simple groups \Orth_{2m+1}(p^n) and PSp_{2m}(p^n) are "good" for p>2 and the simple groups E_7(p^n) are ``good'' for p>3 in the sense of Isaacs, Malle and Navarro. We also describe the action of the diagonal and field automorphisms on the semisimple and the regular characters.
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