2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214444We review the Deligne-Simpson problem, a combinatorial structure of middle convolutions and their relation to a Kac-Moody root system discoverd by Crawley-Boevey. We show with examples that middle convolutions transform the Fuchsian systems with a fixed number of accessory parameters into fundamental systems whose spectral type is in a finite set and we give an explicit connection formula for solutions of Fuchsian differential equations without moduli.23pages, added appendix and examplesClassical Analysis and ODEs34M35text