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arXiv · 1908.08794

On Universal Eigenvalues of Casimir Operator

M. Avetisyan
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Abstract

Motivated by the universal knot polynomials in the gauge Chern-Simons theory, we show that the values of the second Casimir operator on an arbitrary power of Cartan product of $X_2$ and adjoint representations of simple Lie algebras can be represented in a universal form. We show that it complies with $N\longrightarrow -N$ duality of the same operator for $SO(2n)$ and $Sp(2n)$ algebras (the part of $N\leftrightarrow-N$ duality of gauge $SO(2n)$ and $Sp(2n)$ theories). We discuss the phenomena of non-zero universal values of Casimir operator on zero representations.

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M. Avetisyan. 2019-08-22. On Universal Eigenvalues of Casimir Operator. https://doi.org/10.1134/s1547477120050039

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