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1992•Journal of Physics A Mathematical and GeneralOpen access

An efficient algorithm for evaluating the standard Young-Yamanouchi orthogonal representation with two-column Young tableaux for symmetric groups

Wei Wu, Qianer Zhang

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Abstract

An efficient algorithm for evaluating the standard Young-Yamanouchi orthogonal representation with two-column Young tableaux for symmetric groups is presented. The representation matrix is given as the product of three matrices, where two of them are in triangular form, and are determined by an irreducible representation of the symmetric group, and the other is made up of the elements which equal 1, 0 or -1 according to some simple rules.

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An efficient algorithm for evaluating the standard Young-Yamanouchi orthogonal representation with two-column Young tableaux for symmetric groups is presented. The representation matrix is given as the product of three matrices, where two of them are in triangular form, and are determined by an irreducible representation of the symmetric group, and the other is made up of the elements which equal 1, 0 or -1 according to some simple rules.

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Available abstract

An efficient algorithm for evaluating the standard Young-Yamanouchi orthogonal representation with two-column Young tableaux for symmetric groups is presented. The representation matrix is given as the product of three matrices, where two of them are in triangular form, and are determined by an irreducible representation of the symmetric group, and the other is made up of the elements which equal 1, 0 or -1 according to some simple rules.

Key concepts: Young tableau, Representation theory of the symmetric group, Representation (politics), Symmetric group, Representation theory of finite groups, Combinatorics, Irreducible representation, Mathematics

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