Free-field realization of theWKP(N) algebra

TheW_KP^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW_KP^(N) can also be decomposed toN independent copies ofW_KP⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW_KP⁽¹⁾. In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW_KP^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R)_k algebras with levelk = 1. By reductions, we give similar results forW^(N) andW₃⁽²⁾ algebra.