期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1991
卷号：88
期号：19
页码：8415-8419
DOI：10.1073/pnas.88.19.8415
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Although a great deal of work has gone into construction of the irreducible representations of the symmetric group n (and of the general linear group) a simple, intuitive characterization of the symmetry classes is missing. Relying on a systematic distinction between permutations of variables and permutations of places, we provide two such characterizations, showing that elements belonging to any such symmetry class can be described in one of two ways: (i) as the solutions of explicitly given (though not independent) sets of linear equations or (ii) as linear combinations of "simple" elements of a given symmetry class, a simple element being a generalization to an arbitrary symmetry class of the notion of a decomposable skew-symmetric tensor.
