P-partitions and a multi-parameter Klyachko idempotent

Details P-partitions and a multi-parameter Klyachko idempotent P-partitions and a multi-parameter Klyachko idempotent

2005-09-06

arxiv.org/abs/math/0509125v2

Electronic Journal of Combinatorics 11(2) (2005), #R21

Mathematics

Combinatorics

16 pages, 1 figure. Final version: incorporates suggestions of the referee, no changes to the results

Scientific paper

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,..., 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.

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