Zonal polynomial
In mathematics, a zonal polynomial is a multivariate symmetric homogeneous polynomial. The zonal polynomials form a basis of the space of symmetric polynomials.
They appear as zonal spherical functions of the Gelfand pairs (here, is the hyperoctahedral group) and , which means that they describe canonical basis of the double class algebras and .
They are applied in multivariate statistics.
The zonal polynomials are the case of the C normalization of the Jack function.
References
- Robb Muirhead, Aspects of Multivariate Statistical Theory, John Wiley & Sons, Inc., New York, 1984.
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