The AKNS Hierarchy Integrability Analysis Revisited: The Vertex Operator Approach and its Lie-Algebraic Structure

A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised. The relationship with the Lie-algebraic integrability scheme is analyzed, the connection with the tau-function representation is briefly discussed.