On Some Aspects of the Deligne–Simpson Problem

The Deligne-Simpson problem in the multiplicative version is formulated as follows: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ∈ GL(n, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{C}$$ \end{document}), so that there exist irreducible (p + 1)-tuples of matrices Mj ∈ Cjsatisfying the equality M1 . . . Mp+1 = I.