A case study in finite groups; PSL sub 2 (F sub 7 )
- Service de Physique Theorique de Saclay, F-91191 Gif-sur-Yvette Cedex (FR)
Recent investigations on the classification of rational conformal theories have suggested relations with finite groups. It is not known at present if this is more than a happy coincidence in simple cases or possibly some more profound link exploiting the analogy between fusion rules and decompositions of tensor products of group representations or even in a more abstract context q-deformations of Lie algebras for roots of unity. Although finite group theory is a very elaborate subject the authors review on a slightly non-trivial example some of its numerous aspects, in particular those related to rings of invariants. The hope was to grasp, if possible, some properties which stand a chance of being related to conformal theories. Subgroups of SU(2) were found to be related to the A-D-E classification of Wess-Zumino-Witten models based on the corresponding affine Lie algebra. Extending the investigations to SU(3) the authors have picked one of its classical subgroups as a candidate of interest.
- OSTI ID:
- 6404652
- Journal Information:
- Modern Physics Letters B; (USA), Vol. 5:16; ISSN 0217-9849
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONFORMAL INVARIANCE
CLASSIFICATION
ALGEBRAIC FIELD THEORY
FIELD ALGEBRA
FINITE-RANGE INTERACTIONS
GROUP THEORY
LIE GROUPS
PARTITION FUNCTIONS
SU-2 GROUPS
SU-3 GROUPS
AXIOMATIC FIELD THEORY
FIELD THEORIES
FUNCTIONS
INTERACTIONS
INVARIANCE PRINCIPLES
MATHEMATICS
QUANTUM FIELD THEORY
SU GROUPS
SYMMETRY GROUPS
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