Abstract
In a realization of the Kac-Moody algebra A 2 (1) intermediate between the homogeneous and the principal realization, an integrable hierarchy of differential equations is constructed. The hierarchy shares features of both the AKNS and the KdV hierarchies. The same hierarchy can also be constructed using the Drinfeld-Sokolov approach in terms of zero curvature conditions, with as hamiltonian structure the W 3 (2) algebra of Polyakov and Bershadsky. It provides evidence for the conjecture that there exists a general relation between hierarchies constructed in some intermediate realization and the covariantly coupled chiral algebras of Bais, Tjin and van Driel.
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