On the existence of monodromy groups of Fuchsian systems on Riemann's sphere with unipotent generators (Q1972705)

Here, the following Deligne-Simpson problem is considered: For what choice of the \((p+1)\)-tuple of conjugacy classes \(C_1,\dots, C_{p+1}\) in \(\text{GL}(n,\mathbb{C})\), \(p\geq 2\), do there exist irreducible \((p+1)\)-tuples of matrices \(M_j\in C_j\) such that \(M_1,\dots, M_{p+1}= I\), \(I\) being the identity matrix? Necessary and sufficient conditions for the existence of such tuples in the case where \(M_j\) are unipotent are investigated.