W-Symmetry of the Adelic Grassmannian
Representation Theory
2015-05-13 v1 Algebraic Geometry
Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.0807.4992,
title = {W-Symmetry of the Adelic Grassmannian},
author = {David Ben-Zvi and Thomas Nevins},
journal= {arXiv preprint arXiv:0807.4992},
year = {2015}
}