Calculation and Properties of Zonal Polynomials

被引：0
|
作者：
Lin Jiu
Christoph Koutschan
机构：
[1] Dalhousie University,Department of Mathematics and Statistics
[2] Austrian Academy of Sciences,Johann Radon Institute for Computational and Applied Mathematics (RICAM)
来源：
Mathematics in Computer Science | 2020年 / 14卷
关键词：
Zonal polynomial; Symmetric function; Integer partition; Laplace–Beltrami operator; Wishart matrix; Hypergeometric function of a matrix argument; Primary 05E05; Secondary 33C20; 33C70; 15B52; 65C60;
D O I：
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中图分类号：
学科分类号：
摘要：
We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, representation theory, and combinatorics. We present two computer algebra packages, in SageMath and in Mathematica, for their computation. With the help of these software packages, we carry out an experimental mathematics study of some properties of zonal polynomials. Moreover, we derive and prove closed forms for several infinite families of zonal polynomial coefficients.
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页码：623 / 640
页数：17
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