Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: W-symmetries on the Homogeneous Space G/U(1)^r   A construction of $W$-symmetries is given only in terms of the nonlocal
fields (parafermions ${\ps}_{\al}$), which take values on the homogeneous space
$G/U(1)^r$, where $G$ is a simply connected compact Lie group manifold (its
accompanying Lie algebra ${\cal G}$ is a simple one of rank $r$). Only certain
restriction of the root set of Lie algebra on which the parafermionic fields
take values are satisfied, then a consistent and non-trivial extension of the
stress momentum tensor may exist. For arbitrary simple-laced algebras, i.e. the
$A-D-E$ cases, a more detailed discussion is given. The OPE of spin three
primary field are calculated, in which a primary field with spin four is
emerging.

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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: hep-ex