On the expansion of \(C^*_{\rho}(V+I)\) as a sum of zonal polynomials
type: Item
instance of: scholarly article
title: On the expansion of \(C^*_{\rho}(V+I)\) as a sum of zonal polynomials
zbMATH Open document ID: 0584.62103
DOI: 10.1016/0047-259X(85)90096-X
author: H. B. Kushner
published in: Journal of Multivariate Analysis
publication date: 1985-01-01T00:00:00Z
review text: The coefficients \(a_{\tau \rho}\), sometimes called ''generalized binomial coefficients'' in the expansion \(C^*_{\rho}(V+I)=\sum_{\tau}a_{\rho \tau}C^*_{\tau}(V)\), are computed explicitly when \(t=r+1\), where \(\rho\) is a partition of r and \(\tau\) a partition of t. A recursion formula permits the calculation of the general \(a_{\tau \rho}\). Several properties of \(a_{\tau \rho}\) are proved. A connection between the \(a_{\tau \rho}\) and other coefficients is established. The main tools used are Bingham's identity, results from the theory of invariant differential operators, and a lemma concerning zonal polynomials.
Mathematics Subject Classification ID: 62H99
Mathematics Subject Classification ID: 33E99
zbMATH DE Number: 3936262
zbMATH Keywords: generalized binomial coefficients
zbMATH Keywords: recursion formula
zbMATH Keywords: Bingham's identity
zbMATH Keywords: invariant differential operators
zbMATH Keywords: zonal polynomials
MaRDI profile type: Publication
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full work available at URL: 0047-259x(85)90096-x
OpenAlex ID: W1558562449
description: scientific article; zbMATH DE number 3936262