BEYOND THE FRENKEL-KAC-SEGAL CONSTRUCTION OF AFFINE LIE-ALGEBRAS

This contribution reviews recent progress in constructing affine Lie a lgebras at arbitrary level in terms of vertex operators. The string mo del describes a completely compactified subcritical chiral bosonic str ing whose momentum lattice is taken to be the (Lorentzian) affine weig ht lattice. The main feature of the new realization is the replacement of the ordinary string oscillators by physical DDF operators, whereas the unphysical position operators are substituted by certain linear c ombinations of the Lorentz generators. As a side result we obtain simp le expressions for the affine Weyl translations as Lorentz boosts. Var ious applications of the construction are discussed.