$X_2$ series of universal quantum dimensions
High Energy Physics - Theory
2018-12-20 v1 Mathematical Physics
math.MP
Representation Theory
Abstract
The antisymmetric square of the adjoint representation of any simple Lie algebra is equal to the sum of adjoint and representations. We present universal formulae for quantum dimensions of an arbitrary Cartan power of . They are analyzed for singular cases and permuted universal Vogel's parameters. has been the only representation in the decomposition of the square of the adjoint with unknown universal series. Application to universal knot polynomials is discussed.
Keywords
Cite
@article{arxiv.1812.07914,
title = {$X_2$ series of universal quantum dimensions},
author = {M. Y. Avetisyan and R. L. Mkrtchyan},
journal= {arXiv preprint arXiv:1812.07914},
year = {2018}
}
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33 pages