Quantum cohomology and the periodic Toda lattice

Martin A. Guest; Takashi Otofuji

doi:10.1007/PL00005552

Quantum cohomology and the periodic Toda lattice

Martin A. Guest^*, Takashi Otofuji

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kähler 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.

Original language	English
Pages (from-to)	475-487
Number of pages	13
Journal	Communications in Mathematical Physics
Volume	217
Issue number	3
DOIs	https://doi.org/10.1007/PL00005552
Publication status	Published - 2001 Mar
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/PL00005552

Cite this

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title = "Quantum cohomology and the periodic Toda lattice",

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N2 - We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kähler 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.

AB - We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kähler 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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U2 - 10.1007/PL00005552

DO - 10.1007/PL00005552

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JF - Communications in Mathematical Physics

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ER -

Quantum cohomology and the periodic Toda lattice

Abstract

ASJC Scopus subject areas

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