Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal
  SL(2,R)/U(1) Model --- The Classical and Quantum Cases   We give a unified description of our recent results on the the
inter-relationship between the integrable infinite KP hierarchy, nonlinear
$\hat{W}_{\infty}$ current algebra and conformal noncompact $SL(2,R)/U(1)$
coset model both at the classical and quantum levels. In particular, we present
the construction of a quantum version of the KP hierarchy by deforming the
second KP Hamiltonian structure through quantizing the $SL(2,R)_k/U(1)$ model
and constructing an infinite set of commuting quantum $\hat{W}_{\infty}$
charges (at least at $k$=1).

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph