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arXiv · 1603.09068

Higher level vertex operators for $U_q (\hat{\mathfrak{sl}}_2)$

Slaven Kozic
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Abstract

We study graded nonlocal $\underline{\mathsf{q}}$-vertex algebras and we prove that they can be generated by certain sets of vertex operators. As an application, we consider the family of graded nonlocal $\underline{\mathsf{q}}$-vertex algebras $V_{c,1}$, $c\geq 1$, associated with the principal subspaces $W(c\Lambda_0)$ of the integrable highest weight $U_q (\hat{\mathfrak{sl}}_2)$-modules $L(c\Lambda_0)$. Using quantum integrability, we derive combinatorial bases for $V_{c,1}$ and compute the corresponding character formulae.

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Slaven Kozic. 2016-03-30. Higher level vertex operators for $U_q (\hat{\mathfrak{sl}}_2)$. https://doi.org/10.1007/s00029-017-0348-0

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