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math-ph2026
Uniqueness of universal quantum dimensions
M. Y. Avetisyan, R. L. Mkrtchyan
We prove, under some assumptions, the uniqueness of universal quantum dimension formulae. We first show that the quantum dimensions of classical algebras have a specific form that…
math-ph2021
On linear resolvability of universal quantum dimensions
M. Y. Avetisyan, R. L. Mkrtchyan
In his study of finite (Vassiliev's) knot invariants,Vogel introduced the so-called universal parameters, belonging to the projective plane, which particularly parameterize the sim…
math-ph2019
On universal quantum dimensions of certain two-parameter series of representations
M. Y. Avetisyan, R. L. Mkrtchyan
We present the universal, in Vogel's sense, expression for the quantum dimension of Cartan product of an arbitrary number of adjoint and representations of simple Lie algebra…