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Tilted irreducible representations of the permutation group. (English) Zbl 0873.20013

Summary: 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 \(\beta\) satisfying a reduced characteristic equation of the form \((\beta-I)^k=0\). A distinctive feature of the approach is that the non-zero matrix elements are restricted to \(\pm 1\). A so-called natural representation is obtained by multiplying each representation matrix by \(\beta^{-1}\). Alternatively the representation property of the matrices is maintained by inserting the matrix \(\beta^{-1}\) between two representation matrices.

MSC:

20C40 Computational methods (representations of groups) (MSC2010)
20C30 Representations of finite symmetric groups
Full Text: DOI

References:

[1] Biedenharn, L. C., (Lectures in Theoretical Physics, Vol V (1963), Interscience Publishers: Interscience Publishers New York) · Zbl 0173.53802
[2] Soto, M. F.; Mirman, R., Comput. Phys. Commun., 23, 95 (1981)
[3] Littlewood, D. E., The Theory of Group Characters and Matrix Representations of Groups (1958), Clarendon Press: Clarendon Press Oxford · Zbl 0079.03604
[4] James, G.; Kerber, A., The Representation Theory of the Symmetric Group (1981), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0491.20010
[5] Soto, M. F.; Mirman, R., Comput. Phys. Commun., 27, 57 (1982)
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