  Let $(E)$ be a homogeneous linear differential equation Fuchsian of order $n$
over $\mathbb{P}^{1}(\mathbb{C}) $. The idea of Riemann (1857) was to obtain
the properties of solutions of ($E$) by studying the local system. Thus, he
obtained some properties of Gauss hypergeometric functions by studying the
associated rank 2 local system over $\mathbb{P}^{1}(\mathbb{C}) \backslash\{3
points\} $. For example, he obtained the Kummer transformations of the
hypergeometric functions without any calculation. The success of the Riemann's
methods is due to the fact that the irreducible rank 2 local system over
$\mathbb{P}^{1}(\mathbb{C}) \backslash\{3 points\} $ is linearly "rigid" in the
sense of Katz \cite{Katz}. This result constitute one of the best studied
example of linear rigid system, it was proved by the Levelt's theorem \cite{B}
Theorem 1.2.3. In this work we propose a partial generalization of the Levelt's
theorem.
