[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j190625

EXAMPLES OF SIMPLY REDUCIBLE GROUPS

Luan, Yongzhi (Department of Mathematics The Hong Kong University of Science and Technology)

Publication Information

Journal of the Korean Mathematical Society / v.57, no.5, 2020 , pp. 1187-1237 More about this Journal

Abstract

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.

Keywords

Simply reducible group; ambivalence; multiplicity-free; Kronecker multiplicity; Clebsch-Gordan coefficient;

Citations & Related Records

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