Abstract
We give a geometric construction of the W1+∞ vertex algebra as the infinitesimal form of a factorization structure on an adèlic Grassmannian. This gives a concise interpretation of the higher symmetries and Bäcklund-Darboux transformations for the KP hierarchy and its multicomponent extensions in terms of a version of "W1+∞-geometry": the geometry of D-bundles on smooth curves, or equivalently torsion-free sheaves on cuspidal curves.
Original language | English (US) |
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Pages (from-to) | 185-204 |
Number of pages | 20 |
Journal | Communications in Mathematical Physics |
Volume | 293 |
Issue number | 1 |
DOIs | |
State | Published - 2009 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics