WAKIMOTO REALIZATION OF THE ELLIPTIC QUANTUM GROUP $U_{q,p}(\widehat{{\rm sl}_N})$

We construct a free field realization of the elliptic quantum algebra [Formula: see text] for arbitrary level k ≠ 0, -N. We study Drinfeld current and the screening current associated with [Formula: see text] for arbitrary level k. In the limit p → 0 this realization becomes q-Wakimoto realization for [Formula: see text].

ℏ (YANGIAN) DEFORMATION OF THE MIURA MAP AND VIRASORO ALGEBRA

An ℏ-deformed Virasoro Poisson algebra is obtained using the Wakimoto realization of the Sugawara operator for the Yangian double DYℏ( sl 2)c at the critical level c=-2.

AN EXPLICIT CONSTRUCTION OF WAKIMOTO REALIZATIONS OF CURRENT ALGEBRAS

It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra [Formula: see text] can be associated with each parabolic subalgebra [Formula: see text] of the Lie algebra [Formula: see text], where in the standard case [Formula: see text] is the Cartan and [Formula: see text] 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 [Formula: see text]-valued current in terms of symplectic bosons belonging to [Formula: see text] and a current belonging to [Formula: see text]. 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.

A FREE FIELD REPRESENTATION OF THE SCREENING CURRENTS OF $U_q (\widehat{{\rm sl}(3)})$

We construct five independent screening currents associated with the [Formula: see text] quantum current algebra. The screening currents are expressed as exponentials of the eight basic deformed bosonic fields that are required in the quantum analog of the Wakimoto realization of the current algebra. Four of the screening currents are "simple," in that each one is given as a single exponential field. The fifth is expressed as an infinite sum of exponential fields. For reasons which we will discuss, we expect that the structure of the screening currents for a general quantum affine algebra will be similar to the [Formula: see text] case.

GAUSS DECOMPOSITION, WAKIMOTO REALIZATION AND GAUGED WZNW MODELS

The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to the standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging and Abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an Abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables.