Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Baxter's Q-operator for the W-algebra $W_N$   The q-oscillator representation for the Borel subalgebra of the affine
symmetry $U_q(sl_N^)$ is presented. By means of this q-oscillator
representation, we give the free field realizations of the Baxter's Q-operator
$Q_j(t)$, $\bar{Q}_j(t)$ for the W-algebra $W_N$. We give the functional
relations of the $T$-$Q$ operators, including the higher-rank generalization of
the Baxter's $T$-$Q$ relation.

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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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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: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph