Maximal supersymmetry and exceptional groups

Journal article, 2010

The article is a tribute to my old mentor, collaborator and friend Murray Gell-Mann. In it I describe work by P. Ramond, S.-S. Kim and myself where we describe the N = 8 supergravity in the light-cone formalism. We show how the Cremmer-Julia E-7(7) nonlinear symmetry is implemented and how the full supermultiplet is a representation of the E-7(7) symmetry. I also show how the E-7(7) symmetry is a key to understand the higher order couplings in the theory and is very useful when we discuss possible counterterms for this theory.