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Differential operators associated with zonal polynomials. II

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Summary

LetC κ(S) be the zonal polynomial of the symmetricm×m matrixS=(sij), corresponding to the partition κ of the non-negative integerk. If ∂/∂S is them×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 ofk. 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.

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  1. Donald St. P. Richards

    Present address: the University of North Carolina, USA

Authors and Affiliations

  1. University of the West Indies, UK

    Donald St. P. Richards

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  1. Donald St. P. Richards
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Richards, D.S.P. Differential operators associated with zonal polynomials. II. Ann Inst Stat Math 34, 119–121 (1982). https://doi.org/10.1007/BF02481013

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  • DOI: https://doi.org/10.1007/BF02481013

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