Quantum cohomology and the periodic Toda lattice

Martin Guest, Takashi Otofuji

Research output: Contribution to journalArticle

4 Citations (Scopus)


We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kähler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. We derive a simple and explicit "differential operator formula" for the necessary quantum products, which applies both to the finite-dimensional and to the infinite-dimensional situations.

Original languageEnglish
Pages (from-to)475-487
Number of pages13
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - 2001 Mar
Externally publishedYes


ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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