论文标题
奇怪的谎言表示的多个倒数
The plethystic inverse of the odd Lie representations
论文作者
论文摘要
$ lie_n的Frobenius特征，$ $ SYMETRIC GROUP $ s_n $的表示，由Free Lie代数的多连线组件提供，众所周知，可以满足许多有趣的杂质身份。在本文中，我们证明了理查德·史丹利（Richard Stanley）的猜想，建立了奇数谎言特征的总和$ \ sum_ {n \ geq 0} lie_ {2n+1} $的多个倒数。我们从钩子索引的不可减数和谎言表示方面，获得了$ s_n $的常规表示的显而易见的新的分解。我们确定了奇数谎言特征的交替总和的多个逆。
The Frobenius characteristic of $Lie_n,$ the representation of the symmetric group $S_n$ afforded by the multilinear component of the free Lie algebra, is known to satisfy many interesting plethystic identities. In this paper we prove a conjecture of Richard Stanley establishing the plethystic inverse of the sum $\sum_{n\geq 0} Lie_{2n+1}$ of the odd Lie characteristics. We obtain an apparently new plethystic decomposition of the regular representation of $S_n$ in terms of irreducibles indexed by hooks, and the Lie representations. We determine the plethystic inverse of the alternating sum of the odd Lie characteristics.
