\(P\)-partitions and a multi-parameter Klyachko idempotent
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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.
@article{10_37236_1878,
author = {Peter McNamara and Christophe Reutenauer},
title = {\(P\)-partitions and a multi-parameter {Klyachko} idempotent},
journal = {The electronic journal of combinatorics},
year = {2004},
volume = {11},
number = {2},
doi = {10.37236/1878},
zbl = {1162.17301},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1878/}
}
Peter McNamara; Christophe Reutenauer. \(P\)-partitions and a multi-parameter Klyachko idempotent. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1878
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