Discrete faithful representation conjecture for cycle Artin groups in irreducible symmetric spaces

Let $X=G/K$ be an irreducible symmetric space of rank at least two, let $F$ be a maximal flat in $X$, and let $p_0\in F$. A geodesic in $F$ through $p_0$ is singular if it has the singularity property used in the paper. Let $A(C_n)$ denote the Artin group associated to the cycle graph with $n$ vertices. Representation conjecture. If there are at least three singular geodesics in $F$ passing through $p_0$, then there are infinitely many conjugacy classes of discrete, faithful representations of $A(C_n)$ into $G$ for every $n\geq 6$. If $X$ has rank two and exactly two singular geodesics in $F$ pass through $p_0$, then there are infinitely many conjugacy classes of discrete, faithful representations of $A(C_{2n})$ into $G$ for every $n\geq 3$. The claim proposes a broad existence result for representations constructed from configurations of singular geodesics; the preceding discussion identifies obstructions in certain symmetric spaces, while the conjectured cases remain unresolved in the supplied text.