$X_2$ series of universal quantum dimensions

M. Y. Avetisyan; R. L. Mkrtchyan

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arXiv · 1812.07914

$X_2$ series of universal quantum dimensions

M. Y. Avetisyan·R. L. Mkrtchyan

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Abstract

The antisymmetric square of the adjoint representation of any simple Lie algebra is equal to the sum of adjoint and $X_2$ representations. We present universal formulae for quantum dimensions of an arbitrary Cartan power of $X_2$. They are analyzed for singular cases and permuted universal Vogel's parameters. $X_2$ 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.

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M. Y. Avetisyan, R. L. Mkrtchyan. 2018-12-19. $X_2$ series of universal quantum dimensions. https://arxiv.org/abs/1812.07914

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