Graphical Models of Characters of Groups |
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Authors: | Shinsaku Fujita Sherif El-Basil |
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Institution: | (1) Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, 606-8585, Japan;(2) Faculty of Pharmacy, Kasr El-Aini Street, Cairo, Egypt, 11562 |
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Abstract: | A graphical method of generating one- and (some) two-dimensional characters ( ) has been developed on the basis of a reduced homomer set, which has been derived from a new concept of negative graphs. Thus, a homomer set HG(/G
i
)]={h1,...,h
d–1,h
d
} (d=|G|/|G
i
|) has been generated from a regular body of G so that it has been governed by the coset representation G(/G
i
). The homomer set has been reduced into a reduced homomer set ![hamilt](/content/p978240824131486/xxlarge8459.gif) ![prime](/content/p978240824131486/xxlarge8242.gif) ]={h1,...,h
d–1}, where we have placed h
d
–(h1+![sdot](/content/p978240824131486/xxlarge8901.gif) ![sdot](/content/p978240824131486/xxlarge8901.gif) +h
d–1) in terms of negative graphs. The action of the symmetry operations of G on the reduced homomer set ![hamilt](/content/p978240824131486/xxlarge8459.gif) ![prime](/content/p978240824131486/xxlarge8242.gif) ] has graphically generated a one- or (some) two-dimensional character ( ). The versatility of the graphical method has been tested by using C
3v
, D
2h
, C
2h
, C
2v
, D
3h
, and C
3h
as examples. The graphical method has been compared with an alternative algebraic generation using marks (or markaracters), i.e., =G(/G
i
)–G(/G). |
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Keywords: | |
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