Irreducible representations of the symmetry groups of polymers. IV. The relevant subset of a line group
- 1 September 1982
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 15 (9) , 2661-2664
- https://doi.org/10.1088/0305-4470/15/9/016
Abstract
For pt.III see ibid., vol.14, p.1825-34, (1981). The irreducible representations of the line groups (constructed in the preceding papers of this series) provide a useful labelling scheme for electron energy bands of stereo-regular polymers and quasi one-dimensional solids. To implant automatic symmetry assignation into a band-structure computing routine one needs a method of dealing with representations of line groups, which are of infinite order. The author demonstrates that the set K of coset representatives of the translational subgroup T of the line group L-which has a finite (and usually quite small) number of elements-contains all the relevant information. Dealing only with K, one can complete the symmetry assignation, decompose a reducible representation and derive selection rules.Keywords
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