Flat Structure on the Space of Isomonodromic Deformations
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 a Frobenius manifold structure. In this paper, we study isomonodromic deformations of an Ok...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2020 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2020
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211010 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Flat Structure on the Space of Isomonodromic Deformations. Mitsuo Kato, Toshiyuki Mano and Jiro Sekiguchi. SIGMA 16 (2020), 110, 36 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 a Frobenius manifold structure. In this paper, we study isomonodromic deformations of an Okubo system, which is a special kind of system 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 a Frobenius manifold. As a 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.
|
|---|---|
| ISSN: | 1815-0659 |