Weyl groups for non-classical restricted Lie algebras and the Chevalley restriction theorem
Weyl groups for non-classical restricted Lie algebras and the Chevalley restriction theorem
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DOI：
10.1515/forum-2011-0145
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发表时间：
2010-03
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影响因子：
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通讯作者：
J. Bois;Rolf Farnsteiner;B. Shu
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文献类型：
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作者：
J. Bois;Rolf Farnsteiner;B. Shu
设（g，[p]）是定义在特征p>0的代数闭域k上的有限维限制李代数. g的最大维数环面的方案产生一个有限群S（g），它与g的Weyl群重合，如果g是经典型李代数。本文计算了Cartan型李代数的群S（g），并给出了它在权空间分解、通有环面的存在性和多项式不变量等方面的应用。
Let (g,[p]) be a finite-dimensional restricted Lie algebra, defined over an algebraically closed field k of characteristic p>0. The scheme of tori of maximal dimension of g gives rise to a finite group S(g) that coincides with the Weyl group of g in case g is a Lie algebra of classical type. In this paper, we compute the group S(g) for Lie algebras of Cartan type and provide applications concerning weight space decompositions, the existence of generic tori and polynomial invariants.