Let $G$ be the fundamental group of the complement of the torus knot of type $(m,n)$. We study the relationship between $SU(2)$ and $\sldos$-representations of this group, looking at their characters. Using the description of the character variety of $G$, $X(G)$, we give a geometric description of $Y(G)\subset X(G)$, the set of characters arising from $SU(2)$-representations.
"The $SU(2)$-character varieties of torus knots." Rocky Mountain J. Math. 45 (2) 583 - 600, 2015. https://doi.org/10.1216/RMJ-2015-45-2-583