由单李群的杂交特征标产生的高斯体积
Gaussian cubature arising from hybrid characters of simple Lie groups
摘要：
具有两个不同根长的李群允许在其对应的Weyl群上有两个混合符号同态，这又产生了两族混合Weyl群轨道函数和特征标。在本文中，我们扩展的想法导致高斯求积公式的多项式族所产生的字符的不可约表示的任何简单的李群，新的求积公式的基础上相应的混合字符。这些公式在短根情况下是高斯体积的新形式，在长根情况下是Radau体积的新形式。体积的节点很自然地产生于李群的有限阶元素（计算效率高）。
英文摘要：
Lie groups with two different root lengths allow two mixed sign homomorphisms on their corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit functions and characters. In this paper we extend the ideas leading to the Gaussian cubature formulas for families of polynomials arising from the characters of irreducible representations of any simple Lie group, to new cubature formulas based on the corresponding hybrid characters. These formulas are new forms of Gaussian cubature in the short root length case and new forms of Radau cubature in the long root case. The nodes for the cubature arise quite naturally from the (computationally efficient) elements of finite order of the Lie group.
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