Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $W_{\infty}$ Algebras in the Quantum Hall Effect   We show that a large class of incompressible quantum Hall states correspond
to different representations of the \Winf algebra by explicit construction of
the second quantized generators of the algebra in terms of fermion and vortex
operators. These are parametrized by a set of integers which are related to the
filling fraction. The class of states we consider includes multilayer Hall
states and the states proposed by Jain to explain the hierarchical filling
fractions. The corresponding second quantized order parameters are also given.

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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con