  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.
