PreprintHigher level vertex operators for \(U_q (\widehat{\mathfrak{sl}}_2)\)Slaven KožićAbstractWe 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 \(U_q (\widehat{\mathfrak{sl}}_2)\)modules \(L(c\Lambda_0)\). Using quantum integrability, we derive combinatorial bases for \(V_{c,1}\) and compute the corresponding character formulae. This paper is available as a pdf (592kB) file.
