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

Slaven Kožić

Abstract

We study graded nonlocal $\underset{―}{\mathsf{q}}$-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 $\underset{―}{\mathsf{q}}$-vertex algebras $V_{c,1}$, $c\ge 1$, associated with the principal subspaces $W(c{\mathrm{\Lambda }}_0)$ of the integrable highest weight $U_q({\widehat{\mathfrak{sl}}}_2)$-modules $L(c{\mathrm{\Lambda }}_0)$. Using quantum integrability, we derive combinatorial bases for $V_{c,1}$ and compute the corresponding character formulae.