Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realizations of simple affine vertex algebras and their modules: the
  cases $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$   We study embeddings of the simple admissible affine vertex algebras
$V_k(sl(2))$ and $V_k(osp(1,2))$, $k \notin {\Bbb Z}_{\ge 0}$, into the tensor
product of rational Virasoro and $N=1$ Neveu-Schwarz vertex algebra with
lattice vertex algebras.
  We prove that the admissible affine vertex algebra $V_k(sl(2))$ can be
embedded into vertex algebra $L^{Vir} (c_{p,p'}, 0) \otimes \Pi(0)$ where
  $L^{Vir} (c_{p,p'}, 0) $ is suitable minimal Virasoro vertex algebra and
$\Pi(0)$ is a vertex algebra of lattice type.
  By using these realizations we construct a family of weight, logarithmic and
Whittaker $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$--modules. As an
application, we construct all irreducible degenerate Whittaker modules for
$V_k(sl(2))$.

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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex