Free Boson Realization of $U_q(\widehat{s{l}_N})$

Abstract

We construct a realization of the quantum affine algebra $U_q(\widehat{s{l}_N})$ of an arbitrary level $k$ in terms of free boson fields. In the $q\to 1$ limit this realization becomes the Wakimoto realization of $\widehat{s{l}_N}$. The screening currents and the vertex operators(primary fields) are also constructed; the former commutes with $U_q(\widehat{s{l}_N})$ modulo total difference, and the latter creates the $U_q(\widehat{s{l}_N})$ highest weight state from the vacuum state of the boson Fock space.

24 pages, LaTeX, RIMS-924, YITP/K-1018