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Orthogonal Group Matrices of Hyperoctahedral Groups

Published online by Cambridge University Press:  22 January 2016

J. S. Frame
J. S. Frame*
Affiliation:
Michigan State University
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The hyperoctahedral group Gn of order 2nn! is generated by permutations and sign changes applied to n digits, d = 1, 2,…, n. The 2n sign changes generate a normal subgroup ∑n whose factor group Gn/∑n is isomorphic with the symmetric group Sn of order n!. To each irreducible orthogonal representation ‹X; μ› of Gn corresponds an ordered pair of partitions [λ] of l and [μ] of m, where l+m = n.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 585 - 590
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Ferns, H. H., The Irreducible Representations of a Group and its Fundamental Regions, Trans. Roy. Soc. Can., Ser 3, Sec. Ill, vol. 28, 1934.Google Scholar
[2] Frame, J. S., The Constructive Reduction of Finite Group Representations, Proc. of Symposia in Pure Math. (1960 Institute on Finite Groups) vol. VI, pp. 89–99.Google Scholar
[3] Frame, J. S., Robinson, G. de B., and Thrall, R. M., The hook graphs of the symmetric group, Can. Jour. Math., vol. 6 (1954), pp. 316–324.CrossRefGoogle Scholar
[4] Robinson, G. de B., Representation Theory of the Symmetric Group, University of Toronto Press, 1961. Especially pp. 35–38.Google Scholar