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This paper is devoted to the study of the uniformization of the moduli spaceof pairs (X, E) consisting of an algebraic curve and a vector bundle on it. Forthis goal, we study the moduli space of 5-tuples (X, x, z, E, \phi), consistingof a genus g curve, a point on it, a local coordinate, a rank n degree d vectorbundle and a formal trivialization of the bundle at the point. A group actingon it is found and it is shown that it acts (infinitesimally) transitively onthis moduli space and an identity between central extensions of its Lie algebrais proved. Furthermore, a geometric explanation for that identity is offered.

Uniformization of the Moduli Space of Pairs Consisting of a Curve and a Vector Bundle