Geodesic
Zonal polynomials for wreath products
Journal of Algebraic Combinatorics, Tome 25 (2007) no. 2, pp. 189-215.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The pair of groups, symmetric group $S _{2 n }$ and hyperoctohedral group $H _{ n }$, form a Gelfand pair. The characteristic map is a mapping from the graded algebra generated by the zonal spherical functions of $( S _{2 n }, H _{ n })$ into the ring of symmetric functions. The images of the zonal spherical functions under this map are called the zonal polynomials. A wreath product generalization of the Gelfand pair $( S _{2 n }, H _{ n })$ is discussed in this paper. Then a multi-partition versions of the theory is constructed. The multi-partition version of zonal polynomials are products of zonal polynomials and Schur functions and are obtained from a characteristic map from the graded Hecke algebra into a multipartition version of the ring of symmetric functions.
Keywords: keywords zonal polynomial, Schur function, Gelfand pair, Hecke algebra, hypergeometric function 
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     title = {Zonal polynomials for wreath products},
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Mizukawa, Hiroshi. Zonal polynomials for wreath products. Journal of Algebraic Combinatorics, Tome 25 (2007) no. 2, pp. 189-215. http://geodesic.mathdoc.fr/item/JAC_2007__25_2_a2/