  The Deligne-Simpson problem is formulated like this: give necessary and
sufficient conditions for the choice of the conjugacy classes $C_j\subset
SL(n,{\bf C})$ or $c_j\subset sl(n,{\bf C})$ so that there exist irreducible
$(p+1)$-tuples of matrices $M_j\in C_j$ or $A_j\in c_j$ satisfying the equality
$M_1... M_{p+1}=I$ or $A_1+... +A_{p+1}=0$. We solve the problem for generic
eigenvalues with the exception of the case of matrices $M_j$ when the greatest
common divisor of the numbers $\Sigma_{j,l}(\sigma)$ of Jordan blocks of a
given matrix $M_j$, with a given eigenvalue $\sigma$ and of a given size $l$
(taken over all $j$, $\sigma$, $l$) is $>1$. Generic eigenvalues are defined by
explicit algebraic inequalities. For such eigenvalues there exist no reducible
$(p+1)$-tuples. The matrices $M_j$ and $A_j$ are interpreted as monodromy
operators of regular linear systems and as matrices-residua of fuchsian ones on
Riemann's sphere.
