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Induced representations of the full holosymmetric double space groups based on the body-centred cubic bravais lattice

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  • Kunert, H.
  • Suffczyński, M.

Abstract

We introduce a modified formula for the element matrices of the induced representations of any crystallographic space group. With the help of this formula we can obtain all the induced representations of any space group. The generating matrices of the induced representations for the groups Im3m ( O9h) and Ia3d ( O10h) have been calculated. In particular, we have considered the representations corresponding to high-symmetry points in the Brillouin zone. For these two space groups we give explicitly the generators and generating relations for the full irreducible representations induced from the small irreducible representations of Miller and Love. A program, written in ALGOL for the computer ODRA 1204, computes from the generating relations and from the generators the induced unitary irreducible representations of the little and full wave vector groups at high symmetry points. The matrices of the full irreducible representations of the full space groups are needed for the construction of the invariants involved in the theory of second-order phase transitions.

Suggested Citation

  • Kunert, H. & Suffczyński, M., 1982. "Induced representations of the full holosymmetric double space groups based on the body-centred cubic bravais lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 600-603.
    • Handle: RePEc:eee:phsmap:v:114:y:1982:i:1:p:600-603
    DOI: 10.1016/0378-4371(82)90357-0
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