Abstract
In this chapter, we discuss how to construct irreducible representations of a group from the known representations of its invariant subgroup. This problem reduces to the construction of irreducible ray representations with an appropriate factor system. The treatment will be most easily understood by working through it for some point group. The representation theory for space groups is a typical application of the scheme developed in this chapter.
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References
The following paper gives a slightly different treatment: W. G. Harter: J. Math. Phys. 10,739 (1969)
T. Janssen: Crystallographic Groups (North-Holland, Amsterdam 1973) pp. 243–254
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© 1990 Springer-Verlag Berlin Heidelberg
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Inui, T., Tanabe, Y., Onodera, Y. (1990). Representations of a Group II. In: Group Theory and Its Applications in Physics. Springer Series in Solid-State Sciences, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80021-4_5
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DOI: https://doi.org/10.1007/978-3-642-80021-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60445-7
Online ISBN: 978-3-642-80021-4
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