THE IRREDUCIBLE REPRESENTATIONS OF THE LINE GROUPS
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Date
1955
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Ohio State University
Abstract
The symmetries of chain molecules are described by line groups, one-dimensional space groups. The irreducible representation matrices of such groups are obtainable by methods devised by Seitz and elaborated by others. The line group is first expanded in cosets based on the translational invariant subgroup. Diagonal matrices for the translational operations of the line group are built up from irreducible representations of the Abelian translation group. Their dimensionalities are determined from the properties of the basis eigenfunctions of the line group. The coset representatives for nontranslational operations are obtained from certain line group properties. There will be in general several line group representations corresponding to each set of translation matrices. These may all be obtained with the aid of certain subgroups to the line groups. A modified procedure is necessary for line groups containing glide planes or screw axes. Representation matrices are constructed for several line groups, and their irreducibility and completeness are demonstrated. The application of these results to the factoring of the secular equation of chain molecules is discussed.
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Author Institution: General Research Organization, The Olin Mathicson Chemical Corporation