紧单李群有穷级元表示的正交多项式的求积公式
Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups
摘要：
本文包含一个推广的已知性质的切比雪夫多项式的第二类在一个变量的多项式的$n$变量的根格的基础上的紧凑的单李群$G$的任何类型和秩$n$。这些结果受H. Li和Y. Xu在那里他们从$A$型格导出体积公式，基于$G$中有穷级的正则元素产生的插值点，为每个单李群$G$产生高斯体积公式。多项式产生于$G$的不可约特征和作为这些特征的某些有限子集的公共零点的插值点。李的理论方法的一贯使用揭示了中心思想清楚，并允许一个简单的统一发展的主题。此外，它指出了真正的，也许是深远的谎言理论联系。
英文摘要：
The paper contains a generalization of known properties of Chebyshev polynomials of the second kind in one variable to polynomials of $n$ variables based on the root lattices of compact simple Lie groups $G$ of any type and of rank $n$. The results, inspired by work of H. Li and Y. Xu where they derived cubature formulae from $A$-type lattices, yield Gaussian cubature formulae for each simple Lie group $G$ based on interpolation points that arise from regular elements of finite order in $G$. The polynomials arise from the irreducible characters of $G$ and the interpolation points as common zeros of certain finite subsets of these characters. The consistent use of Lie theoretical methods reveals the central ideas clearly and allows for a simple uniform development of the subject. Furthermore it points to genuine and perhaps far reaching Lie theoretical connections.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
