P-partitions and a multi-parameter Klyachko idempotent

McNamara, Peter et Reutenauer, Christophe (2005). « P-partitions and a multi-parameter Klyachko idempotent ». The electronic journal of combinatorics, 11(2), R21-1-R21-18.

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Résumé

Because they play a role in our understanding of the symmetric group algebra, Lie idempotents have received considerable attention. The Klyachko idempotent has attracted interest from combinatorialists, partly because its definition involves the major index of permutations. For the symmetric group Sn, we look at the symmetric group algebra with coefficients from the field of rational functions in n variables q1, . . . ,qn. In this setting, we can define an n-parameter generalization of the Klyachko idempotent, and we show it is a Lie idempotent in the appropriate sense. Somewhat surprisingly, our proof that it is a Lie element emerges from Stanley's theory of P-partitions.

Type: Article de revue scientifique
Mots-clés ou Sujets: Klyachko idempotent, Lie idempotent, symmetric group algebra
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Christophe Reutenauer
Date de dépôt: 19 avr. 2016 18:27
Dernière modification: 27 avr. 2016 18:31
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8193

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