Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A $\hbar$-deformation of the $W_{N}$ algebra and its vertex operators   In this paper,we derive a $\hbar$-deformation of the $W_{N}$ algebra and its
quantum Miura tranformation. The vertex operators for this $\hbar$-deformed
$W_{N}$ algebra and its commutation relations are also obtained.

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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: comp-gas
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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: quant-ph
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The categories of this paper are: econ
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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: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th