  We show that multivariable colored link invariants are derived from the roots
of unity representations of $U_q(g)$. We propose a property of the
Clebsch-Gordan coefficients of $U_q(g)$, which is important for defining the
invariants of colored links. For $U_q(sl_2) we explicitly prove the property,
and then construct invariants of colored links and colored ribbon graphs, which
generalize the multivariable Alexander polynomial.
