Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: W-Symmetry of the Adelic Grassmannian   We give a geometric construction of the W_{1+infty} vertex algebra as the
infinitesimal form of a factorization structure on an adelic Grassmannian. This
gives a concise interpretation of the higher symmetries and Backlund-Darboux
transformations for the KP hierarchy and its multicomponent extensions in terms
of a version of "W_{1+infty}-geometry": the geometry of D-bundles on smooth
curves, or equivalently torsion-free sheaves on cuspidal curves.

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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ