Abstract
We consider formulae for universal (in Vogel’s sense) quantum dimensions and their applications. Universal quantum dimensions of Cartan powers of \({{X}_{2}}\) 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.
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ACKNOWLEDGMENTS
The work of MA is fulfilled within the Regional Doctoral Program on Theoretical and Experimental Particle Physics Program sponsored by Volkswagen Stiftung. The work of MA and RM is partially supported by the Science Committee of the Ministry of Science and Education of the Republic of Armenia under contract 18T-1C229.
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Avetisyan, M.Y., Mkrtchyan, R.L. Universality and Quantum Dimensions. Phys. Part. Nuclei Lett. 17, 784–788 (2020). https://doi.org/10.1134/S1547477120050040
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DOI: https://doi.org/10.1134/S1547477120050040