1998/12/22 by Martin A. Guest, Guest, Martin A., Takashi Otofuji +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA) #math.DG #math.QA
paper · pdf · doi:10.48550/arxiv.math/9812127
17 pages, AMS-TeX. Minor corrections, several additional comments and references
arxiv created 2000/02/16 · arxiv updated 2009/11/30
We 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.