P-划分与多参数Klyachko幂等元
P-partitions and a multi-parameter Klyachko idempotent
摘要：
由于李幂等元在我们理解对称群代数中起着重要的作用，因此受到了相当大的关注。Klyachko幂等元吸引了组合学家的兴趣，部分原因是它的定义涉及置换的主指数。对于对称群S_n，我们考察系数来自n元有理函数域q_1，.的对称群代数，q_n。在这种情况下，我们可以定义一个n参数推广的Klyachko幂等元，我们证明它是一个李幂等元在适当的意义。有点令人惊讶的是，我们的证明，这是一个李元素出现在斯坦利的理论的P-分区。
英文摘要：
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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