Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some vertex algebras related to $V_{-1}(\frak{sl} (n) )$ and their
  characters   We consider several vertex operator (super)algebras closely related to
$V_{-1}(\frak{sl} (n) )$, $n \ge 3$ : (a) the parafermionic subalgebra
$K(\frak{sl}(n),-1)$ for which we completely describe its inner structure, (b)
the vacuum algebra $\Omega (V_{-1}(\frak{sl} (n) ) )$, and (c) an infinite
extension $\mathcal U$ of $V_{-1}(\frak{sl} (n) )$ constructed by combining
certain irreducible ordinary modules with integral weights. It turns out that
$\mathcal U$ is isomorphic to the coset vertex algebra $\frak{psl}(n|n) _1 /
\frak{sl}(n)_1$, $n \ge 3$. We show that $V_{-1}(\frak{sl}(n))$ admits
precisely $n$ ordinary irreducible modules, up to isomorphism. This leads to
the conjecture that ${\mathcal U}$ is {\em quasi-lisse}. We present evidence in
support of this conjecture: we prove that the (super)character of $\mathcal U$
is quasi-modular of weight one by virtue of being the constant term of a
meromorphic Jacobi form of index zero. Explicit formulas and MLDE for
characters and supercharacters are given for $\frak{g}=\frak{sl}(3)$ and
outlined for general $n$. We present a conjectural family of 2nd order MLDEs
for characters of vertex algebras $\frak{psl}(n|n) _1$, $n \geq 2$. We finish
with a theorem pertaining to characters of $\frak{psl}(n|n)_1$ and $\mathcal
U$-modules.

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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas