Tilted irreducible representations of the permutation group

• Published in: Computer physics communications Vol. 86; no. 1; pp. 97 - 104
• Main Author: Bergdolt, G.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1995; Elsevier
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/0010-4655(95)00009-5

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.