Geodesic
Katriel's operators for products of conjugacy classes of $\frak S_n$
Journal of Algebraic Combinatorics, Tome 21 (2005) no. 2, pp. 137-146.

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

Summary: We define a family of differential operators indexed with fixed point free partitions. When these differential operators act on normalized power sum symmetric functions $qlambda$(x), the coefficients in the decomposition of this action in the basis $qlambda$(x) are precisely those of the decomposition of products of corresponding conjugacy classes of the symmetric group S $_{n}$. The existence of such operators provides a rigorous definition of Katriel $rsquo$s elementary operator representation of conjugacy classes and allows to prove the conjectures he made on their properties.
Keywords: keywords conjugacy classes, symmetric functions, operator, structure constants 
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     title = {Katriel's operators for products of conjugacy classes of $\frak S_n$},
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Goupil, Alain; Poulalhon, Dominique; Schaeffer, Gilles. Katriel's operators for products of conjugacy classes of $\frak S_n$. Journal of Algebraic Combinatorics, Tome 21 (2005) no. 2, pp. 137-146. http://geodesic.mathdoc.fr/item/JAC_2005__21_2_a4/