Orthogonal sets of Young symmetrizers

被引：6

作者：

Stembridge, John R. ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

ADVANCES IN APPLIED MATHEMATICS | 2011年 / 46卷 / 1-4期

基金：

美国国家科学基金会;

关键词：

Young symmetrizer; Young tableaux;

D O I：

10.1016/j.aam.2009.08.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Young symmetrizers are primitive idempotents in the group algebra of the symmetric group S-n that are indexed in a natural way by Young tableaux. Although the Young symmetrizers corresponding to standard tableaux may be used to decompose the group algebra into a direct sum of minimal left ideals, they are not pairwise orthogonal in general. We pose the problem of finding maximum sets of pairwise orthogonal (but not necessarily standard) Young symmetrizers, and show in particular that it is possible to find (nonstandard) complete orthogonal sets for all partitions of n if and only if n <= 6. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：576 / 582

页数：7