2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77881We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kaehler 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.17 pages, AMS-TeX. Minor corrections, several additional comments and referencesQuantum AlgebraDifferential Geometrytext