Universality and Quantum Dimensions

We consider formulae for universal (in Vogel’s sense) quantum dimensions and their applications. Universal quantum dimensions of Cartan powers of and adjoint representations at the points of special type singularities are shown to give correct answers when restricted to both exceptional and one othe...

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Bibliographic Details
Published in:Physics of particles and nuclei letters 2020-09, Vol.17 (5), p.784-788
Main Authors: Avetisyan, M. Y., Mkrtchyan, R. L.
Format: Article
Language:English
Subjects:
Lie groups
Particle and Nuclear Physics
Physics
Physics and Astronomy
Physics of Elementary Particles and Atomic Nuclei. Theory
Representations
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Summary:We consider formulae for universal (in Vogel’s sense) quantum dimensions and their applications. Universal quantum dimensions of Cartan powers of and adjoint representations at the points of special type singularities are shown to give correct answers when restricted to both exceptional and one other appropriate lines. Derivation of Diophantine equations, classifying simple Lie algebras, from the universal quantum dimension of the adjoint representation is presented.
ISSN:1547-4771
1531-8567
DOI:10.1134/S1547477120050040