  We 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.
