Classical invariant theory for finite reflection groups
Classical invariant theory for finite reflection groups
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有限反射群的经典不变理论
DOI：
10.1007/bf01235938
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发表时间：
1997
影响因子：
0.7
通讯作者：
M. Hunziker
中科院分区：
文献类型：
--
作者：
M. Hunziker
我们给出了经典反射群（包括二面体群）的任意多个向量变量中的不变多项式代数生成元的显式系统。作为结果的应用，我们证明了经典李代数的 Chevalley 限制定理的推广。在有趣的情况下，当群是 Coxeter 型 Dn (n≥4) 时，我们使用 Wallach 引入的更高极化算子。生成器系统中元素度数的最小上限与向量变量的数量无关。我们推测对于特殊的反射群也是如此，然后为 F4 型群画出一个证明。
We give explicit systems of generators of the algebras of invariant polynomials in arbitrary many vector variables for the classical reflection groups (including the dihedral groups). As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras. In the interesting case when the group is of Coxeter typeDn (n≥4) we use higher polarization operators introduced by Wallach. The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables. We conjecture that this is also true for the exceptional reflection groups and then sketch a proof for the group of typeF4.