UNIQUENESS OF THE BOSONIZATION OF THE UQ(SU(2)K) QUANTUM CURRENT-ALGEBRA

Four apparently different bosonizations of the U(q)(su(2)k) quantum cu rrent algebra for arbitrary level k have recently been proposed in the literature. However, the relations among them have so far remained un clear except in one case. Assuming a special standard form for the U(q )(su(2)k) quantum currents, we derive a set of general consistency equ ations that must be satisfied. As particular solutions of this set of equations, we recover two of the four bosonizations and we derive a ne w and simpler one. Moreover, we show that the latter three, and the re maining two bosonizations which cannot be derived directly from this s et of equations since by construction they do not have the standard fo rm, are all related to each other through some redefinitions of their Heisenberg boson oscillators.