The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups
| Autor: | Kaoru Ikeda |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Weyl group
Pure mathematics High Energy Physics::Lattice General Physics and Astronomy Lie group High Energy Physics::Theory symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems Bruhat decomposition symbols Generalized flag variety Geometry and Topology Gauge theory Orbit (control theory) Mathematics::Representation Theory Toda lattice Mathematical Physics Gauge symmetry Mathematics |
| Zdroj: | Journal of Geometry and Physics. 148:103558 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2019.103558 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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