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Simply reducible groups are important in physics and chemistry, which contain some of the important groups in condensed matter physics and crystal symmetry. By studying the group structures and irreducible representations, we find some new examples of simply reducible groups, namely, dihedral groups, some point groups, some dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic $2$, some Clifford groups, and some Coxeter groups. We give the precise decompositions of product of irreducible characters of dihedral groups, Heisenberg groups, and some Coxeter groups, giving the Clebsch-Gordan coefficients for these groups. To verify some of our results, we use the computer algebra systems GAP and SAGE to construct and get the character tables of some examples.
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참고문헌 (84)
참고문헌 신청
ahulpke / Use GAP to dene nite Cliord group, Mathematics Stack Exchange / Mathematics Stack Exchange
G. E. Andrews / 1998 / The Theory of Partitions / Cambridge Mathematical Library, Cambridge University Press
I. Armeanu / 2014 / About the Schur index for ambivalent groups / Comm. Algebra 42(2):540~544
M. Artin / 2011 / Algebra / Pearson Education, Inc
M. Aschbacher / 2011 / The classication of nite simple groups / Mathematical Surveys and Monographs 172
G. E. Andrews / 1998 / The Theory of Partitions / Cambridge Mathematical Library, Cambridge University Press
I. Armeanu / 2014 / About the Schur index for ambivalent groups / Comm. Algebra 42(2):540~544
M. Artin / 2011 / Algebra / Pearson Education, Inc
M. Aschbacher / 2011 / The classication of nite simple groups / Mathematical Surveys and Monographs 172
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