A Relation Between Schur P and S Functions

Abstract

We define a differential operator of infinite order which sends Schur S- functions to Schur P -functions. Using the properties of \Delta we deduce algebraic identities satisfied by the cardinalities of certain sets of tableaux. R'esum'e --- Nous d'efinissons un op'erateur diff'erentiel d'ordre infini qui envoie les fonctions S de Schur sur les fonctions P de Schur. A l'aide des propri'et'es de \Delta, nous d'eduisons des identit'es alg'ebriques satisfaites par les cardinalit'es de certains ensembles de tableaux. 1 Introduction The subject of this paper is to describe a differential operator \Delta which sends a Schur S-function s to a Schur P -function P c() where c() is a composition associated to the partition by an easy combinatorial method. The definition of \Delta was motivated by the results of [5]. Using the properties of \Delta, we can then deduce algebraic identities satisfied by the cardinalities of certain sets of tableaux (Yamanouchi tableaux, Yamanouchi domino table..