P-Partitions and a Multi-Parameter Klyachko Idempotent

Authors

Peter McNamara, Bucknell UniversityFollow
Christophe Reutenauer

Publication Date

2005

Description

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 S_n we look at the symmetric group algebra with coefficients from the field of rational functions in n variables q₁, q₂, ... , q_n. 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.

Journal

Electronic Journal of Combinatorics

Volume

11

Issue

2

First Page

R21

Department

Mathematics

Recommended Citation

McNamara, Peter and Reutenauer, Christophe. "P-Partitions and a Multi-Parameter Klyachko Idempotent." Electronic Journal of Combinatorics (2005) : R21.