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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 110, 36 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.110
(Mi sigma1647)
 

This article is cited in 10 scientific papers (total in 10 papers)

Flat Structure on the Space of Isomonodromic Deformations

Mitsuo Katoa, Toshiyuki  Manob, Jiro Sekiguchic

a Department of Mathematics, College of Educations, University of the Ryukyus, Japan
b Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Japan
c Department of Mathematics, Faculty of Engineering, Tokyo University of Agriculture and Technology, Japan
References:
Abstract: Flat structure was introduced by K. Saito and his collaborators at the end of 1970's. Independently the WDVV equation arose from the 2D topological field theory. B. Dubrovin unified these two notions as Frobenius manifold structure. In this paper, we study isomonodromic deformations of an Okubo system, which is a special kind of systems of linear differential equations. We show that the space of independent variables of such isomonodromic deformations can be equipped with a Saito structure (without a metric), which was introduced by C. Sabbah as a generalization of Frobenius manifold. As its consequence, we introduce flat basic invariants of well-generated finite complex reflection groups and give explicit descriptions of Saito structures (without metrics) obtained from algebraic solutions to the sixth Painlevé equation.
Keywords: flat structure, Frobenius manifold, WDVV equation, complex reflection group, Painlevé equation.
Funding agency Grant number
Japan Society for the Promotion of Science 25800082
17K05335
26400111
17K05269
This work was partially supported by JSPS KAKENHI Grant Numbers 25800082, 17K05335, 26400111, 17K05269.
Received: March 19, 2020; in final form October 21, 2020; Published online November 3, 2020
Bibliographic databases:
Document Type: Article
Language: English
Citation: Mitsuo Kato, Toshiyuki Mano, Jiro Sekiguchi, “Flat Structure on the Space of Isomonodromic Deformations”, SIGMA, 16 (2020), 110, 36 pp.
Citation in format AMSBIB
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\by Mitsuo~Kato, Toshiyuki ~Mano, Jiro~Sekiguchi
\paper Flat Structure on the Space of Isomonodromic Deformations
\jour SIGMA
\yr 2020
\vol 16
\papernumber 110
\totalpages 36
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\crossref{https://doi.org/10.3842/SIGMA.2020.110}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85096372034}
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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