### 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 |
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Pages (from-to) | 475-487 |

Number of pages | 13 |

Journal | Communications in Mathematical Physics |

Volume | 217 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2001 Mar |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Guest, M. A., & Otofuji, T. (2001). Quantum cohomology and the periodic Toda lattice.

*Communications in Mathematical Physics*,*217*(3), 475-487. https://doi.org/10.1007/PL00005552