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Central Characters and Conjugacy Classes of the Symmetric Group or On some Conjectures of J. Katriel

In: Formal Power Series and Algebraic Combinatorics

Author

Listed:
  • Alain Goupil

    (LaCIM, Université du Québec à Montréal)

  • Dominique Poulalhon

    (École Polytechnique, LIX)

  • Gilles Schaeffer

    (LORIA, CNRS)

Abstract

Résumé Nous démontrons plusieurs conjectures dues à Jacob Katriel sur les classes de conjugaison de S n . La première exprime, pour un partage fixé ρ de la forme r1 n−r , les valeurs propres (ou caractères centraux) ω ρ λ en terme des contenus de ρ. Tandis que Katriel a conjecturé une forme générique et un algorithme pour calculer les coefficients indéterminés, nous fournissons une formule explicite. La seconde conjecture (présentée au SFCA'98 à Toronto) donne une forme générale pour l’expression d’une classe de conjugaison en terme d’opérateurs élémentaires. Nous la prouvons en utilisant une description en termes d’opérateurs différentiels sur les polynômes symétriques. Finalement nous étendons partiellement nos résultats sur ω ρ λ à des partages ρ quelconques.

Suggested Citation

  • Alain Goupil & Dominique Poulalhon & Gilles Schaeffer, 2000. "Central Characters and Conjugacy Classes of the Symmetric Group or On some Conjectures of J. Katriel," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 238-249, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_21
    DOI: 10.1007/978-3-662-04166-6_21
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