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

Yoshitaka Koyama
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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.

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Yoshitaka Koyama. 1996-05-20. Bosonization of Admissible Representations of $U_q(\widehat{sl}_2)$ at Level $-\frac{1}{2}$ and $q$-Vertex Operators. https://arxiv.org/abs/q-alg/9605029

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