Representations of a Group II

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 78)


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.


Irreducible Representation Brillouin Zone Point Group Factor System Vector Representation 
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  1. 5.1
    The following paper gives a slightly different treatment: W. G. Harter: J. Math. Phys. 10,739 (1969)MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 5.2
    T. Janssen: Crystallographic Groups (North-Holland, Amsterdam 1973) pp. 243–254Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Japan Women’s UniversityBunkyo-ku, Tokyo 112Japan
  2. 2.Department of Physics, School of Science and TechnologyMeiji UniversityTama-ku, Kawasaki 214Japan

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