Supersymmetric string theories, superconformal algebras and exceptional groups

We study the relation between extended space-time supersymmetry and extended worldsheet symmetries within the context of four-dimensional heterotic string theories. It is shown how these symmetries follow from an underlying E7 and E8 symmetry which also explains the appearance of extra U(1) gauge bosons. Supersymmetry transformation aalways act within a given multiplet of E7 and E8