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We prove that, given a smooth projective curve C of genus g≥2, the forgetful morphism 
(respectively 
) from the moduli space of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles over C is an embedding. Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.
