Application of coset representations to the construction of symmetry adapted functions |
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Authors: | Shinsaku Fujita |
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Institution: | (1) Research Laboratories, Ashigara, Fuji Photo Film Co., Ltd., Minami-Ashigara, 250-01 Kanagawa, Japan |
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Abstract: | Summary A coset representation (G(/G
i
)), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG
i
, is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G
i
) orbit belongs to theG
i
site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions. |
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Keywords: | Coset representation Regular body Site-symmetry Brester's equation Symmetry adapted functions |
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