  We study the representation theory of the fundamental group of the complement
of a Hopf link with n twists. A general framework is described to analyze the
$SL_r(C)$-representation varieties of these twisted Hopf links as byproduct of
a combinatorial problem and equivariant Hodge theory. As application, close
formulas of their E-polynomials are provided for ranks 2 and 3, both for the
representation and character varieties.
