Symmetric group character degrees and hook numbers
Symmetric group character degrees and hook numbers
复制标题
对称组字符度和钩数
DOI：
10.1112/plms/pdm028
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发表时间：
2007
影响因子：
1.8
通讯作者：
David A. Craven
中科院分区：
文献类型：
--
作者：
David A. Craven
在本文中，我们证明了以下结果：对于任意两个自然数 k 和 ℓ，对于所有足够大的对称群 Sn，存在 k 个不相交的 Sn ℓ 不可约特征集，使得每个集合都由具有相同度的特征组成，并且不同的集合具有不同的度。特别是，这解决了 Moretó 在 [5] 中最近提出的一个猜想。这里使用的方法基于对称群的不可约特征和它们对应的划分之间的对偶性。因此，本文本质上是组合的。
In this article we prove the following result: for any two natural numbers k and ℓ, and for all sufficiently large symmetric groups Sn, there are k disjoint sets of ℓ irreducible characters of Sn, such that each set consists of characters with the same degree, and distinct sets have different degrees. In particular, this resolves a conjecture most recently made by Moretó in [5]. The methods employed here are based upon the duality between irreducible characters of the symmetric groups and the partitions to which they correspond. Consequently, the paper is combinatorial in nature.