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

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.09068
 Bibcode:
 2016arXiv160309068K
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 28 pages, 1 figure