ABSTRACT

The literature on applications of (affine) Kac-Moody Lie groups and algebras is very extensive, see e.g. [Go, GoKO, Her, .\lan, Oli]. Let us also remark that it contains also applications of the Virasoro algebra (the Lie algebra of the universal central extension of the group of diffeomorphisms of the circle [FeiFu]). Let us mention a few types of domains of applications (this list is far from exhaustive): a. Supersymmetry and gravitation, Yang-\lills theory, chiral models: sec,

tions in two dimensions (soliton equations, KP and MKP hierarchies: see, e.g., [Sa, DJK;\1, SeW, KaR]; integrable systems in two dimensions [DJKM, ReSe, SaVe, Sa, deV].