  We describe the geometry of the character variety of representations of the
fundamental group of the complement of a Hopf link with $n$ twists, namely
$\Gamma_{n}=\langle x,y \,| \, [x^n,y]=1 \rangle$ into the group
$\mathrm{SU}(r)$. For arbitrary rank, we provide geometric descriptions of the
loci of irreducible and totally reducible representations. In the case $r = 2$,
we provide a complete geometric description of the character variety, proving
that this $\mathrm{SU}(2)$-character variety is a deformation retract of the
larger $\mathrm{SL}(2,\mathbb{C})$-character variety, as conjectured by
Florentino and Lawton. In the case $r = 3$, we also describe different strata
of the $\mathrm{SU}(3)$-character variety according to the semi-simple type of
the representation.
