Multi-field coset space realizations of w1+∞

The coset space formulation of the one-field realization of w1+∞ is extended to include more fields as the coset parameters. This can be done either by choosing a smaller stability subalgebra in the nonlinear realization of w1+∞ symmetry, or by considering a nonlinear realization of some extended symmetry, or by combining both options. It is shown that all these possibilities give rise to the multi-field realizations of w1+∞. The two-field realization of w1+∞ proceeding is deduced from a coset space of the symmetry group G which is an extension of w1+∞ by the second self-commuting set of higher spin currents. Some multi-field generalizations of the three-field realization are presented and several intriguing parallels with N=2 strings and conformal affine Toda theories are discussed. (author) 16 refs