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Cyclic and dihedral point groups as subgroups of the limiting groups
Author(s) -
Sivardière J.
Publication year - 1981
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221070111
Subject(s) - dihedral angle , limiting , dihedral group , point group , mathematics , pure mathematics , spherical harmonics , group (periodic table) , point (geometry) , crystal (programming language) , field (mathematics) , mathematical analysis , physics , combinatorics , quantum mechanics , geometry , computer science , mechanical engineering , hydrogen bond , molecule , engineering , programming language
Irreducible representations of cyclic and dihedral point groups are deduced from those of the limiting groups ∞ and ∞2. The method is equivalent to that of crystal quantum numbers and gives immediately a classification of spherical harmonics according to the representations of each group. Results are applied to the determination of crystal field splittings and of tensorial invanants and covariants.