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Article
P-Partitions and a Multi-Parameter Klyachko Idempotent
Electronic Journal of Combinatorics
  • Peter McNamara, Bucknell University
  • Christophe Reutenauer
Publication Date
1-1-2005
Volume
11
Issue
2
Disciplines
Abstract
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, q2, ... , 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.
Citation Information
Peter McNamara and Christophe Reutenauer. "P-Partitions and a Multi-Parameter Klyachko Idempotent" Electronic Journal of Combinatorics (2005) p. R21
Available at: http://works.bepress.com/peter_mcnamara/6/