Differential operators associated with zonal polynomials. II

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Abstract

Let C κ(S) be the zonal polynomial of the symmetric m×m matrix S=(sij), corresponding to the partition κ of the non-negative integer k. If ∂/∂S is the m×m matrix of differential operators with (i, j)th entry ((1+δij)∂/∂sij)/2, δ being Kronecker's delta, we show that Ck(∂/∂S)Cλ(S)=k!δλkCk(I), where λ is a partition of k. This is used to obtain new orthogonality relations for the zonal polynomials, and to derive expressions for the coefficients in the zonal polynomial expansion of homogenous symmetric polynomials.

Original languageEnglish (US)
Pages (from-to)119-121
Number of pages3
JournalAnnals of the Institute of Statistical Mathematics
Volume34
Issue number1
DOIs
StatePublished - Dec 1 1982

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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