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

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

1996-05-20

arxiv.org/abs/q-alg/9605029v1

Mathematics

Quantum Algebra

23 pages, LaTex

Scientific paper

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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