Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex operator algebras associated to modular invariant representations
  for $A_1 ^{(1)}$   We investigate vertex operator algebras $L(k,0)$ associated with
modular-invariant representations for an affine Lie algebra $A_1 ^{(1)}$ ,
where k is 'admissible' rational number. We show that VOA $L(k,0)$ is rational
in the category $\cal O$ and find all irreducible representations in the
category of weight modules.

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The categories of this paper are: hep-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph