The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups

Kaoru Ikeda

doi:10.1016/j.geomphys.2019.103558

The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups

Kaoru Ikeda

Faculty of Economics

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

Abstract

In this paper we study the resolution of the singular loci of the generalized Toda lattice on the flag manifold by using blow-up. We define the gauge symmetry of the Weyl group on the fiber of this blow-up. This gauge transformation transforms the singular locus of the Toda lattice on the flag manifold into the face of Weyl chamber. Thus we show that if the orbit of the Toda lattice crosses the singular locus on the flag manifold, then the leap over the face of the Weyl chamber occurs on the fiber.

Original language	English
Article number	103558
Journal	Journal of Geometry and Physics
Volume	148
DOIs	https://doi.org/10.1016/j.geomphys.2019.103558
Publication status	Published - 2020 Feb

Keywords

Bruhat decomposition
Painlevé property
Singular divisor
Split and reductive Lie groups
Toda lattice

ASJC Scopus subject areas

Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology

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title = "The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups",

abstract = "In this paper we study the resolution of the singular loci of the generalized Toda lattice on the flag manifold by using blow-up. We define the gauge symmetry of the Weyl group on the fiber of this blow-up. This gauge transformation transforms the singular locus of the Toda lattice on the flag manifold into the face of Weyl chamber. Thus we show that if the orbit of the Toda lattice crosses the singular locus on the flag manifold, then the leap over the face of the Weyl chamber occurs on the fiber.",

keywords = "Bruhat decomposition, Painlev{\'e} property, Singular divisor, Split and reductive Lie groups, Toda lattice",

author = "Kaoru Ikeda",

note = "Funding Information: I extend my gratitude to Professor Tanisaki, Toshiyuki for his valuable and discerning advice and to referee for appropriate comment. I also thank to Professors Wilfried Schmid because he gave me various ideas for the Gauss decomposition of split reductive Lie groups. This work was supported by Grants-in-aid for Scientific Research of JSPS, Japan. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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language = "English",

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N1 - Funding Information: I extend my gratitude to Professor Tanisaki, Toshiyuki for his valuable and discerning advice and to referee for appropriate comment. I also thank to Professors Wilfried Schmid because he gave me various ideas for the Gauss decomposition of split reductive Lie groups. This work was supported by Grants-in-aid for Scientific Research of JSPS, Japan. Publisher Copyright: © 2019 Elsevier B.V.

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N2 - In this paper we study the resolution of the singular loci of the generalized Toda lattice on the flag manifold by using blow-up. We define the gauge symmetry of the Weyl group on the fiber of this blow-up. This gauge transformation transforms the singular locus of the Toda lattice on the flag manifold into the face of Weyl chamber. Thus we show that if the orbit of the Toda lattice crosses the singular locus on the flag manifold, then the leap over the face of the Weyl chamber occurs on the fiber.

AB - In this paper we study the resolution of the singular loci of the generalized Toda lattice on the flag manifold by using blow-up. We define the gauge symmetry of the Weyl group on the fiber of this blow-up. This gauge transformation transforms the singular locus of the Toda lattice on the flag manifold into the face of Weyl chamber. Thus we show that if the orbit of the Toda lattice crosses the singular locus on the flag manifold, then the leap over the face of the Weyl chamber occurs on the fiber.

KW - Bruhat decomposition

KW - Painlevé property

KW - Singular divisor

KW - Split and reductive Lie groups

KW - Toda lattice

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The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups

Abstract

Keywords

ASJC Scopus subject areas

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