TY - JOUR
T1 - The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups
AU - Ikeda, Kaoru
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.
PY - 2020/2
Y1 - 2020/2
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
UR - http://www.scopus.com/inward/record.url?scp=85075570655&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85075570655&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2019.103558
DO - 10.1016/j.geomphys.2019.103558
M3 - Article
AN - SCOPUS:85075570655
VL - 148
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
SN - 0393-0440
M1 - 103558
ER -