Lie型有限群的建筑物和单模中的对立性
Oppositeness in buildings and simple modules for finite groups of Lie type
摘要：
在李型有限群的构造中，我们考虑由标志的对立性所定义的关联关系。这样的关系导致置换模的同态（在定义特征中），其像是群的单模。关联关系的$p$秩就是这个简单模的维数。我们给出了确定单模特征标的一些一般性约化。它的最高权被确定，问题被减少到一个素域的情况下。约化问题可以通过代数群的表示论来解决，并举例说明了方法。
英文摘要：
In the building of a finite group of Lie type we consider the incidence relations defined by oppositeness of flags. Such a relation gives rise to a homomorphism of permutation modules (in the defining characteristic) whose image is a simple module for the group. The $p$-rank of the incidence relation is then the dimension of this simple module. We give some general reductions towards the determination of the character of the simple module. Its highest weight is identified and the problem is reduced to the case of a prime field. The reduced problem can be approached through the representation theory of algebraic groups and the methods are illustrated for some examples.
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