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We give a new proof of some characteristic-free fundamental theorems in invariant theory rst proved in C. De Concini and C. Procesi, A characteristic free approach to invariant theory, Adv. Math. 21 (1976), 330{354. We treat the action of the general linear group and the symplectic group. Our approach is geometric, and utilizes the fact that the categorical quotients are principal ber bundles o codimension two or more.

Another proof of theorems of De Concini and Procesi