English

Quantum cohomology and the periodic Toda lattice

Quantum Algebra 2007-05-23 v2 Differential Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/9812127,
  title  = {Quantum cohomology and the periodic Toda lattice},
  author = {Martin A. Guest and Takashi Otofuji},
  journal= {arXiv preprint arXiv:math/9812127},
  year   = {2007}
}

Comments

17 pages, AMS-TeX. Minor corrections, several additional comments and references