The construction of Frobenius manifolds from KP tau-functions

J.W. van de Leur; J.W. van de Leur; Ruud Martini

doi:10.1007/s002200050691

The construction of Frobenius manifolds from KP tau-functions

J.W. van de Leur, J.W. van de Leur, Ruud Martini

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Abstract

Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux–Egoroff equations. This system of partial differential equations appears as a specific subset of the n-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions of this Darboux–Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy tau-function can be expressed in the KP tau-function.

Original language	Undefined
Pages (from-to)	587-616
Number of pages	30
Journal	Communications in mathematical physics
Volume	205
DOIs	https://doi.org/10.1007/s002200050691
Publication status	Published - 1999

Keywords

METIS-140617
IR-102319

Access to Document

10.1007/s002200050691

http://dx.doi.org/10.1007/s002200050691

Cite this

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title = "The construction of Frobenius manifolds from KP tau-functions",

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journal = "Communications in mathematical physics",

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N2 - Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux–Egoroff equations. This system of partial differential equations appears as a specific subset of the n-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions of this Darboux–Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy tau-function can be expressed in the KP tau-function.

AB - Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux–Egoroff equations. This system of partial differential equations appears as a specific subset of the n-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions of this Darboux–Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy tau-function can be expressed in the KP tau-function.

KW - METIS-140617

KW - IR-102319

U2 - 10.1007/s002200050691

DO - 10.1007/s002200050691

M3 - Article

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SP - 587

EP - 616

JO - Communications in mathematical physics

JF - Communications in mathematical physics

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