Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ising vectors in the vertex operator algebra $V_{\Lambda}^+$ associated
  with the Leech lattice $\Lambda$   In this article, we study the Ising vectors in the vertex operator algebra
$V_\Lambda^+$ associated with the Leech lattice $\Lambda$. The main result is a
characterization of the Ising vectors in $V_\Lambda^+$. We show that for any
Ising vector $e$ in $V_\Lambda^+$, there is a sublattice $E\cong \sqrt{2}E_8$
of $\Lambda$ such that $e\in V_E^+$. Some properties about their corresponding
$\tau$-involutions in the moonshine vertex operator algebra $V^\natural$ are
also discussed. We show that there is no Ising vector of $\sigma$-type in
$V^\natural$. Moreover, we compute the centralizer $C_{\aut V^\natural}(z,
\tau_e)$ for any Ising vector $e\in V_\Lambda^+$, where $z$ is a 2B element in
$\aut V^\natural$ which fixes $V_\Lambda^+$. Based on this result, we also
obtain an explanation for the 1A case of an observation by Glauberman-Norton
(2001), which describes some mysterious relations between the centralizer of
$z$ and some 2A elements commuting $z$ in the Monster and the Weyl groups of
certain sublattices of the root lattice of type $E_8$ .

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The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: nlin