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A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra. The formulation also allows skew-symmetric as well as symmetric variables. Examples illustrate the scope of this formulation.doi:10.1090/s0002-9947-1989-0986027-x fatcat:nqolvfgrinb2lpiirunzqlkoj4