W-Symmetry of the Adelic Grassmannian

Details W-Symmetry of the Adelic Grassmannian W-Symmetry of the Adelic Grassmannian

2008-07-31

arxiv.org/abs/0807.4992v1

Mathematics

Representation Theory

Scientific paper

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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