Quantum cohomology and the periodic Toda lattice

Martin Guest, Takashi Otofuji

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume217
Issue number3
Publication statusPublished - 2001 Mar
Externally publishedYes

Fingerprint

Quantum Cohomology
Flag Manifold
Toda Lattice
homology
Differential operator
differential operators
Generalise
Necessary
products

ASJC Scopus subject areas

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

Cite this

Quantum cohomology and the periodic Toda lattice. / Guest, Martin; Otofuji, Takashi.

In: Communications in Mathematical Physics, Vol. 217, No. 3, 03.2001, p. 475-487.

Research output: Contribution to journalArticle

Guest, Martin ; Otofuji, Takashi. / Quantum cohomology and the periodic Toda lattice. In: Communications in Mathematical Physics. 2001 ; Vol. 217, No. 3. pp. 475-487.
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