Bosonization of Admissible Representations of $U_q(\widehat{sl}_2)$ at Level $-\frac{1}{2}$ and $q$-Vertex Operators

Abstract

We construct a representation of $U_q(\widehat{sl}_2)$ at level $-1/2$ by using the bosonic Fock spaces. The irreducible modules are obtained as the kernel of a certain operator, in contrast to the construction by Feingold and Frenkel for $q=1$ where such a procedure is not necessary. We also bosonize the $q$-vertex operators associated with the vector representation.