  Given a hyperbolic knot $K$ and any $n\geq 2$ the abelian representations and
the holonomy representation each give rise to an $(n-1)$-dimensional component
in the $\operatorname{SL}(n,\Bbb{C})$-character variety. A component of the
$\operatorname{SL}(n,\Bbb{C})$-character variety of dimension $\geq n$ is
called high-dimensional.
  It was proved by Cooper and Long that there exist hyperbolic knots with
high-dimensional components in the $\operatorname{SL}(2,\Bbb{C})$-character
variety. We show that given any non-trivial knot $K$ and sufficiently large $n$
the $\operatorname{SL}(n,\Bbb{C})$-character variety of $K$ admits
high-dimensional components.
