Completely reducible (2)-homomorphisms
Completely reducible (2)-homomorphisms
复制标题
完全可约 (2)-同态
DOI：
10.1090/s0002-9947-07-04289-4
复制
发表时间：
2005
影响因子：
1.3
通讯作者：
D. Testerman
中科院分区：
文献类型：
--
作者：
George J. McNinch;D. Testerman
设K是任意域，G是K上的半单群。假设K的特性是正的，并且对于G来说非常好。我们描述所有群方案同态Φ：SL 2 → G，其图像在Serre意义上是几何G-完全可约-或G-cr-；该描述类似于斯坦伯格张量积定理给出的不可约模的描述。如果 K 是代数闭且 G 是简单的，这里证明的结果是 Liebeck 和 Seitz 之前使用不同方法得到的。最近的结果显示 Φ 图像的李代数在几何上是 G-cr；这在我们的证明中起着重要作用。
Let K be any field, and let G be a semisimple group over K. Suppose the characteristic of K is positive and is very good for G. We describe all group scheme homomorphisms Φ: SL 2 → G whose image is geometrically G-completely reducible-or G-cr-in the sense of Serre; the description resembles that of irreducible modules given by Steinberg's tensor product theorem. In case K is algebraically closed and G is simple, the result proved here was previously obtained by Liebeck and Seitz using different methods. A recent result shows the Lie algebra of the image of Φ to be geometrically G-cr; this plays an important role in our proof.