Tilted irreducible representations of the permutation group Original Research Article

A fast algorithm to compute irreducible integer representations of the symmetric group is described. The representation is called tilted because the identity is not represented by a unit matrix, but a matrix β satisfying a reduced characteristic equation of the form (β − I)k = 0. A distinctive feature of the approach is that the non-zero matrix elements are restricted to ±1. A so called natural representation is obtained by multiplying each representation matrix by β−1. Alternatively the representation property of the matrices is mantained by inserting the matrix β−1 between two representation matrices.