W-symmetry of the adèlic Grassmannian

David Ben-Zvi, Thomas Nevins

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)185-204
Number of pages20
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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