Quantum cohomology and the periodic Toda lattice

Details Quantum cohomology and the periodic Toda lattice Quantum cohomology and the periodic Toda lattice

1998-12-22

arxiv.org/abs/math/9812127v2

Mathematics

Quantum Algebra

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

Scientific paper

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.

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