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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 toeach finite dimensional representation $V$ of $G$ a vector bundle $\oplus\mathscr{O}(s_i)$ on ${\mathbb P}^1$ with parabolic structure at theramification points. This produces a tensor functor from representation of $G$to vector bundles with parabolic structure that characterises the originalcover. This work attempts to describe this tensor functor in terms of grouptheoretic data. More precisely, we construct a pullback functor on vectorbundles with parabolic structure and describe the parabolic pullback of thepreviously described tensor functor.

Pullback of parabolic bundles and covers of ${\mathbb P}^1\setminus\{0,1,\infty\}$