Among simple infinite-dimensional graded Lie (super)-algebras two are especially interesting for the potential applications. These are the graded algebras that have sl(3) x sl(2) x gl(1), the Lie algebra of symmetries of the Standart Model of Fundamental Particles of the nuclear physics, as their zero degree component.
The talk is based on joint work of the author and V.Kac and will present an approach to constructing the representation theory of these algebras, in particular the generalized Verma modules and complexes of the Verma modules.
