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j symbols and jm factors for all dihedral and cyclic groups

P H Butler and M F Reid

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The methodology of earlier papers by Butler and Wybourne (1976) is used to obtain algebraic formulae for 6j symbols of the double dihedral and cyclic groups and the 3 jm factors for all possible imbeddings: Dm contains/implies Dn and Dm contains/implies Cn. The usual 3 jm symbols of angular momentum theory, that is for SO3 contains/implies SO2, do not have a phase choice which allows their factorisation into SO3 contains/implies Dinfinity and Dinfinity contains/implies SO2 3jm factors. The authors derive the change of phase necessary for factorisation, thus obtaining a relation between SO3 contains/implies Dinfinity factors and the SO3 contains/implies SO2 3jm symbols of standard angular momentum theory. The use of maximal imbeddings has removed the multiplicity problems encountered by other methods.


PACS

02.20.-a Group theory

03.65.Fd Algebraic methods

MSC

16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)

20G42 Quantum groups (quantized function algebras) and their representations (See also 16W35, 17B37, 81R50)

81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 10 (October 1979)



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