### 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 language | English |
---|---|

Pages (from-to) | 475-487 |

Number of pages | 13 |

Journal | Communications in Mathematical Physics |

Volume | 217 |

Issue number | 3 |

Publication status | Published - 2001 Mar |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*217*(3), 475-487.

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 217, no. 3, pp. 475-487.

}

TY - JOUR

T1 - Quantum cohomology and the periodic Toda lattice

AU - Guest, Martin

AU - Otofuji, Takashi

PY - 2001/3

Y1 - 2001/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035531646&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035531646&partnerID=8YFLogxK

M3 - Article

VL - 217

SP - 475

EP - 487

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -