Differential operators associated with zonal polynomials. II

Donald St P. Richards

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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
Issue number1
StatePublished - Dec 1982

All Science Journal Classification (ASJC) codes

  • Statistics and Probability


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