Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher level vertex operators for $U_q (\hat{\mathfrak{sl}}_2)$   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 $U_q
(\hat{\mathfrak{sl}}_2)$-modules $L(c\Lambda_0)$. Using quantum integrability,
we derive combinatorial bases for $V_{c,1}$ and compute the corresponding
character formulae.

32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg