## 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.

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 Tuesday, April 5, 2016