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

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 $V_{c,1}$, $c\ge 1$, 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.

28 pages, 1 figure

References in corpus (5)

• Field Algebras
• Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case
• Principal subspaces for quantum affine algebra $U_q(A_n^{(1)})$
• Vertex operators and principal subspaces of level one for $U_q({\widehat{\mathfrak{sl}}}_2)$
• A note on the zeroth products of Frenkel-Jing operators

Cited by in corpus (1)

• Principal subspaces for the affine Lie algebras in types $D$, $E$ and $F$