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

Slaven Kožić

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 \(U_q (\widehat{\mathfrak{sl}}_2)\)-modules \(L(c\Lambda_0)\). Using quantum integrability, we derive combinatorial bases for \(V_{c,1}\) and compute the corresponding character formulae.