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A maximal extended supergravity lagrangian is constructed in seven dimensions, which exhibits USp(4) ≈ SO(5) local and SL(5, R) global invariances. We find that the antisymmetric second rank tensor fields must possess a generalized gauge invariance in order that the theory is consistent and supersymmetric. We conjecture that the theory might admit SO(5) × SO(5) Yang-Mills symmetries in d = 7 and SO(4) × SO(5) × SO(5) in d = 4 [with the last SO(5), gauging composite fields] after suitable compactification.
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