On SL(3,$\mathbb{C}$)-representations of the Whitehead link group

We describe a family of representations in SL(3,$\mathbb{C}$) of the fundamental group $\pi$ of the Whitehead link complement. These representations are obtained by considering pairs of regular order three elements in SL(3,$\mathbb{C}$) and can be seen as factorising through a quotient of $\pi$ defined by a certain exceptional Dehn surgery on the Whitehead link. Our main result is that these representations form an algebraic component of the SL(3,$\mathbb{C}$)-character variety of $\pi$.