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

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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 languageEnglish
Article number103558
JournalJournal of Geometry and Physics
Volume148
DOIs
Publication statusPublished - 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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