Uniqueness of universal dimensions and configurations of points and lines
Quantum Algebra
2021-06-15 v3 High Energy Physics - Theory
Mathematical Physics
Group Theory
math.MP
Representation Theory
Abstract
The problem of uniqueness of universal formulae for (quantum) dimensions of simple Lie algebras is investigated. We present generic functions, which multiplied by a universal (quantum) dimension formula, preserve both its structure and its values at the points from Vogel's table. Connection of some of these functions with geometrical configurations, such as the famous Pappus-Brianchon-Pascal configuration of points and lines, is established. Particularly, the appropriate realizable configuration (yet to be found) will provide a symmetric non-uniqueness factor for any universal dimension formula.
Keywords
Cite
@article{arxiv.2101.10860,
title = {Uniqueness of universal dimensions and configurations of points and lines},
author = {M. Y. Avetisyan and R. L. Mkrtchyan},
journal= {arXiv preprint arXiv:2101.10860},
year = {2021}
}
Comments
20 pages, 6 Figures