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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 classalgebras and . They are applied in multivariate statistics. The zonal polynomials are the case of the C normalization of the Jack function.
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