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## Main Question or Discussion Point

Does anybody know a simple proof of the fact that there are no finite-dimensional extensions of the [tex]\textsl{so(n)}[/tex]-spinor representation to the group of general linear transformations. The proof seems can be based on the well-known fact that when rotated [tex]2\pi[/tex] a spinor transforms [tex]\psi\rightarrow-\psi[/tex]. But i have found no elementary proof...