  Consider the Deligne-Simpson problem: {\em give necessary and sufficient
conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$
(resp. $c_j\subset gl(n,{\bf C})$) so that there exist irreducible
$(p+1)$-tuples of matrices $M_j\in C_j$ (resp. $A_j\in c_j$) satisfying the
equality $M_1... M_{p+1}=I$ (resp. $A_1+... +A_{p+1}=0$)}. The matrices $M_j$
and $A_j$ are interpreted as monodromy operators and as matrices-residua of
fuchsian systems on Riemann's sphere.
  We give new examples of existence of such $(p+1)$-tuples of matrices $M_j$
(resp. $A_j$) which are {\em rigid}, i.e. unique up to conjugacy once the
classes $C_j$ (resp. $c_j$) are fixed. For rigid representations the sum of the
dimensions of the classes $C_j$ (resp. $c_j$) equals $2n^2-2$.
