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{\bf Peter McNamara and Christophe Reutenauer}
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{\bf $P$-Partitions and a Multi-Parameter Klyachko Idempotent}
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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
$q_1, \ldots, q_n$. 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.
\bye