Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branching Rule Decomposition of Irreducible Level-1 E_6^(1)-modules with
  respect to F_4^(1)   It is well known that using the weight lattice of type $E_6$, $P$, and the
lattice construction for vertex operator algebras one can obtain all three
level 1 irreducible $\tilde{g}$-modules with $V_P = V^{\Lamba_0} \oplus
V^{\Lamba_1} \oplus V^{\Lamba_6}$. The Dynkin diagram of type $E_6$ has an
order 2 automorphism, $\tau$, which can be lifted to $\tilde{{\tau}}$, a Lie
algebra automorphism of $\tilde{g}$ of type $E_6^(1)$. The fixed points of
$\tilde{{\tau}}$ are a subalgebra $\tilde{a}$ of type $F_4^(1)$. The
automorphism $\tau$ lifts further to $\hat{{\tau}}$ a vertex operator algebra
automorphism of $V_P$.
  We investigate the branching rules, how these three modules for the affine
Lie algebra $\tilde{g}$ decompose as a direct sum of irreducible
$\tilde{a}$-modules. To complete the decomposition we use the Godard-Kent-Olive
coset construction which gives a $c = \frac{4}{5}$ module for the Virasoro
algebra on $V_P$ which commutes with $\tilde{a}$. We use the irreducible
modules for this coset Virasoro to give the space of highest weight vectors for
$\tilde{a}$ in each $V^{\Lamba_i}$. The character theory related to this
decomposition is examined and we make a connection to one of the famous
Ramanujan identities. This dissertation constructs coset Virasoro operators
$Y(\omg,z)$ by explicitly determining the generator $\omg$. We also give the
explicit highest weight vectors for each $Vir \otimes F_4^(1)$-module in the
decomposition of each $V^{\Lamba_i}$. This explicit work on determining highest
weight vectors gives some insight into the relationship to the Zamolodchikov
$W_3$-algebra.

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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol