An explicit construction of Wakimoto realizations of current algebras

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It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra Gₖ can be associated with each parabolic subalgebra P=(G₀+ G+) of the Lie algebra G, where in the standard case G₀ is the Cartan and P is the Borel subalgebra. In this letter we obtain an explicit formula for the Wakimoto realization in the general case. Using Hamiltonian reduction of the WZNW model, we first derive a Poisson bracket realization of the G-valued current in terms of symplectic bosons belonging to G+ and a current belonging to G₀. We then quantize the formula by determining the correct normal ordering. We also show that the affine-Sugawara stress-energy tensor takes the expected quadratic form in the constituents.