  We work over an algebraically closed ground field of characteristic zero. A
$G$-cover of ${\mathbb P}^1$ ramified at three points allows one to assign to
each finite dimensional representation $V$ of $G$ a vector bundle $\oplus
\mathscr{O}(s_i)$ on ${\mathbb P}^1$ with parabolic structure at the
ramification points. This produces a tensor functor from representation of $G$
to vector bundles with parabolic structure that characterises the original
cover. This work attempts to describe this tensor functor in terms of group
theoretic data. More precisely, we construct a pullback functor on vector
bundles with parabolic structure and describe the parabolic pullback of the
previously described tensor functor.
