Let G be a reductive group over k, X a connected projective curve over k. Associate to a scheme S over a field k the set M_{G,X}(S) of isomorphism classes of G bundles on S\times X, this defines a contravariant functor from schemes over k to sets which is not representable when G has for instance a nontrivial center, since bundles would admit nontrivial automorphisms. I'm not however able to fully complete the argument which seems vaguely transparent yet tricky. Can someone please comment on what I'm missing?
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