The Deligne-Simpson problem for zero index of rigidity (Q2765970)

Here is the problem: Given conjugacy classes \(c_j\subset{\mathfrak{gl}}(n,\mathbb{C})\) or \(C_j\subset\text{GL}(n,\mathbb{C})\), \(j=1,\dots,p+1\), is there an irreducible \((p+1)\)-tuple of matrices in \(c_j\) (resp., in \(C_j\)) whose sum is 0 (resp., whose product is \(I\)). The negative answer is obtained in the case when the sum of the dimensions of the classes is \(2n^2\).NEWLINENEWLINEFor the entire collection see [Zbl 0971.00014].