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

TL;DR

This paper constructs a family of SL(3,C) representations of the Whitehead link group, showing they form an algebraic component of its character variety, thus advancing understanding of link group representations.

Contribution

It introduces a new family of SL(3,C) representations derived from special elements and identifies them as an algebraic component of the character variety.

Findings

Representations form an algebraic component of the character variety.

Constructed via pairs of regular order three elements in SL(3,C).

Related to a specific Dehn surgery on the Whitehead link.

Abstract

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 $\pi$.