Quantum cohomology and the periodic Toda lattice

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

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Quantum Algebra, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/77881

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9812127
 http://arxiv.org/abs/math/9812127

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arXiv