Gauge deformations of maximal supergravity in D = 11 - n dimensions generically give rise to a tensor hierarchy of p-form fields that transform in specific representations of the global symmetry group E-n. We derive the formulas defining the hierarchy from a Borcherds superalgebra corresponding to E-n. Tiffs explains why the E-n representations in the tensor hierarchies also appear in the level decomposition of the Borcherds superalgebra. We show that the indefinite Kac-Moody algebra E-11 can be used equivalently to determine these representations, up to p = D, and for arbitrarily large p if E-11 is replaced by E-r with sufficiently large rank r.
The work is supported by IISN Belgium (conventions 4.4511.06 and 4.4514.08), by the Belgian Federal Science Policy Office through the Interuniversity Attraction Pole P6/11.