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

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.