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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
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.
Received: March 19, 2020; in final form October 21, 2020; Published online November 3, 2020
Citation:
Mitsuo Kato, Toshiyuki Mano, Jiro Sekiguchi, “Flat Structure on the Space of Isomonodromic Deformations”, SIGMA, 16 (2020), 110, 36 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1647 https://www.mathnet.ru/eng/sigma/v16/p110
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