AbstractSuppose that W is a finite, unitary, reflection group acting on the complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in W, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of W-invariant polynomial functions on V to the algebra of C-invariant functions on X. In this note we consider the special case when W is a Coxeter group, V is the complexified reflection representation of W, and X is in the lattice of the arrangement of W, and give a simple, combinatorial characterization of when the restriction mapping is surjective in terms of the exponents of W and C. As an application of our result, in the case when W is the Weyl group of a semisimple, complex Lie algebra, we complete a calculation begun by Richardson in 1987 and obtain a simple combinatorial characterization of regular decomposition classes whose closure is a normal variety.
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机译：摘要假设W是作用在复矢量空间V上的有限的ary反射群，而X是V的子空间。在W中将N定义为X的逐态稳定器，将Z定义为点向稳定器，并且C = N / Z.然后，限制条件定义了从V上的W不变多项式函数的代数到X上C不变的多项式函数的代数的同态。在本注释中，我们考虑当W是Coxeter群时的特殊情况，V是W的复杂反射表示，并且X在W的排列的晶格中，并给出简单的，组合的刻画，表示约束映射在W和C的指数方面是射影。作为我们的结果的应用，当W是我们完成了由理查森（Richardson）于1987年开始的半简单复Lie代数的Weyl群，并获得了常规分解类的简单组合特征，该类的闭合是正常的。
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