Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices
Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices
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正特征中 Vinberg 的 θ 群和 Kostant-Weierstrass 切片
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发表时间：
2009
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通讯作者：
P. Levy
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作者：
P. Levy
本文将Vinberg θ-群或周期分次约化李代数的基本结果推广到具有良好正特征的域上。为此，我们澄清小Weyl群和（标准）Weyl群之间的关系。我们推出的环的不变量与分次是一个多项式环。这种方法使我们能够证明一个经典的分次李代数（零或奇正特征）的KW-截面的存在性，证实了波波夫在这种情况下的猜想。
We generalize the basic results of Vinberg’s θ-groups, or periodically graded reductive Lie algebras, to fields of good positive characteristic. To this end we clarify the relationship between the little Weyl group and the (standard) Weyl group. We deduce that the ring of invariants associated to the grading is a polynomial ring. This approach allows us to prove the existence of a KW-section for a classical graded Lie algebra (in zero or odd positive characteristic), confirming a conjecture of Popov in this case.