Free field realization of $q$-deformed primary fields for $U_q(\widehat{\sl}_2)$

Abstract

The $q$-vertex operators of Frenkel and Reshetikhin are studied by means of a $q$-deformation of the Wakimoto module for the quantum affine algebra $U_q(\widehat{\sl}_2)$ at an arbitrary level $k\ne 0,-2$. A Fock module version of the $q$-deformed primary field of spin $j$ is introduced, as well as the screening operators which (anti-)commute with the action of $U_q(\widehat{\sl}_2)$ up to a total difference of a field. A proof of the intertwining property is given for the $q$-vertex operators corresponding to the primary fields of spin $j\notin \frac{1}{2}{\mathbb{Z}}_{\ge 0}$, which is enough to treat a general case. A sample calculation of the correlation function is also given.

arXiv comment22 pages

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