Linearly degenerate hierarchies of quasiclassical SDYM type

We demonstrate that SDYM equations for the Lie algebra of one-dimensional vector fields represent a natural reduction in the framework of general linearly degenerate dispersionless hierarchy. We define the reduction in terms of wave functions, introduce generating relation, Lax-Sato equations and the dressing scheme for the reduced hierarchy. Multidimensional case is also discussed.