Jump to content

Zonal polynomial

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by 65.29.219.180 (talk) at 19:50, 24 May 2016 (Undid revision 695765481 by 193.52.94.40 (talk) rvv). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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.