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Duals of crystallographic groups. Band and quasi-band representations

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Abstract

Band representations are analyzed from a pure group theoretical point of view, with the aid of the dual of the crystallographic group (the set of equivalence classes of unitary irreducible representations). It is shown on the examples of the onedimensional crystallographic groups that we have to introduce a distinction between band and quasi-band representations, the wordband being reserved for induced representations.

The dual of the groupF222 is explicitly constructed. It permits to show that two elementary band representations which have the same decompositions into unitary irreducible representations are not equivalent.

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  1. Henri Bacry

    Present address: Centre de Physique Théorique and Faculté des Sciences de Luminy, Case 907, 13288, Marseille, Cedex 8, France

Authors and Affiliations

  1. Department of Physics, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Henri Bacry

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  1. Henri Bacry
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Communicated by A. Connes

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Bacry, H. Duals of crystallographic groups. Band and quasi-band representations. Commun.Math. Phys. 153, 359–390 (1993). https://doi.org/10.1007/BF02096648

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  • DOI: https://doi.org/10.1007/BF02096648

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