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We study the system of equations derived twenty five years ago by B. de Witand the first author [Nucl. Phys. B281 (1987) 211] as conditions for theconsistent truncation of eleven-dimensional supergravity on AdS_4 x S^7 togauged N = 8 supergravity in four dimensions. By exploiting the E_7(7)symmetry, we determine the most general solution to this system at each pointon the coset space E_7(7)/SU(8). We show that invariants of the generalsolution are given by the fluxes in eleven-dimensional supergravity. Thisallows us to both clarify the explicit non-linear ansatze for the fluxes givenpreviously and to fill a gap in the original proof of the consistenttruncation. These results are illustrated with several examples.

Consistent truncation of d = 11 supergravity on AdS_4 x S^7