The Deligne-Simpson problem asks to find a condition on conjugacy classes C1, . . . , Ck ⊂ Matn(C) such that there are matrices Yi ∈ Ci with (1) ∑k i=1 Yi = 0, (2) and there are no proper subspaces in C stable under all Yi. Crawley-Boevey reduced this problem to checking if there is an irreducible representation in Rep(Π(Q), v) for suitable Q, λ, v produced from C1, . . . , Ck. Recall, Section ...