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Article Dans Une Revue Journal of Algebraic Combinatorics / Journal of Algebraic Combinatorics An International Journal Année : 2005

Katriel's operations for products of conjugacy classes of Sn

Résumé

We define a family of differential operators indexed with fixed point free partitions. When these differential operators act on normalized power sums symmetric functions $q_\lambda(x)$, the coefficients in the decomposition of this action in the basis $q_\lambda(x)$ 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's elementary operator representation of conjugacy classes and allows to prove the conjectures he made on their properties.
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Dates et versions

hal-00159311 , version 1 (02-07-2007)

Identifiants

  • HAL Id : hal-00159311 , version 1

Citer

Alain Goupil, Dominique Poulalhon, Gilles Schaeffer. Katriel's operations for products of conjugacy classes of Sn. Journal of Algebraic Combinatorics / Journal of Algebraic Combinatorics An International Journal, 2005, 21 (2), pp.137-146. ⟨hal-00159311⟩
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