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Zonal polynomial
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Zonal polynomial : ウィキペディア英語版
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
(S_,H_n) (here, H_n is the hyperoctahedral group) and (Gl_n(\mathbb),
O_n), which means that they describe canonical basis of the double class
algebras \mathbb(\backslash S_ / H_n ) and \mathbb().
They are applied in multivariate statistics.
The zonal polynomials are the \alpha=2 case of the C normalization of the Jack function.
==References==

* Robb Muirhead, ''Aspects of Multivariate Statistical Theory'', John Wiley & Sons, Inc., New York, 1984.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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