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.