. Dans-cette-partie, En utilisant les identités de Ward associées au courant de spin 3 W (3) (z) et les dégénérescences des modules de ? et ? ?1 , on a montré que ces corrélateurs satisfont uné equation aux dérivées partielles d'ordre deux. Cette EDP peutêtrepeutêtre transformée en uné equation aux valeurs propres de l'hamiltonien de Calogero-Sutherland pour une valeur négative de la constante de couplage ? = ?(k + 1)/(r ? 1) Ceci fournit une preuve de la conjecture reliant les fonctionsàfonctionsà N points des opérateurs parafermioniques ? et ? ?1 aux polynômes de Jack. Comme nous allons le voir dans le chapitre 6, ces polynômes constituent des fonctions d'onde test pour unétatunétat fondamental bosonique au remplissage ? = k/r dans l'effet Hall quantique fractionnaire. Dans ce contexte il est intéressant de considérer aussi lesétatslesétats excités, obtenus en insérant des quasi-trous : les fonctions d'onde correspondantes devraient aussi pouvoir s'exprimer comme des, en insérant des opérateurs de quasi-trou conjecturés commé etant ? = ? (2,1,...1|1,1...1)

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