The Toda flows preserving small cells of the flag variety G / B and Kazhdan's x0-grading

Kaoru Ikeda

doi:10.1016/j.geomphys.2006.06.003

The Toda flows preserving small cells of the flag variety G / B and Kazhdan's x₀-grading

Kaoru Ikeda

Faculty of Economics

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

1 Citation (Scopus)

Abstract

There exist many works on full Kostant-Toda flows whose initial points belong to a grand cell of the flag variety. In this paper we study the full Kostant-Toda flows whose initial points belong to small cells other than the grand cell and preserving small cells. To obtain such flows, we consider the cell decomposition of the grand cell induced by Bruhat decomposition of the flag variety. We show that such full Kostant-Toda flow can be reduced to the ordinary tridiagonal Toda flow by using sheaf theoretical methods.

Original language	English
Pages (from-to)	799-813
Number of pages	15
Journal	Journal of Geometry and Physics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1016/j.geomphys.2006.06.003
Publication status	Published - 2007 Feb

Keywords

Bruhat decomposition
Full Kostant-Toda lattice
Gauss decomposition
Kazhdan's x-grading
Toda lattice

ASJC Scopus subject areas

Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology

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10.1016/j.geomphys.2006.06.003

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title = "The Toda flows preserving small cells of the flag variety G / B and Kazhdan's x0-grading",

abstract = "There exist many works on full Kostant-Toda flows whose initial points belong to a grand cell of the flag variety. In this paper we study the full Kostant-Toda flows whose initial points belong to small cells other than the grand cell and preserving small cells. To obtain such flows, we consider the cell decomposition of the grand cell induced by Bruhat decomposition of the flag variety. We show that such full Kostant-Toda flow can be reduced to the ordinary tridiagonal Toda flow by using sheaf theoretical methods.",

keywords = "Bruhat decomposition, Full Kostant-Toda lattice, Gauss decomposition, Kazhdan's x-grading, Toda lattice",

author = "Kaoru Ikeda",

note = "Funding Information: This study was supported by the 21st Century COE Program at Keio University Integral Mathematical Science and a Grant-in-Aid for Research from JSPS. ",

year = "2007",

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AB - There exist many works on full Kostant-Toda flows whose initial points belong to a grand cell of the flag variety. In this paper we study the full Kostant-Toda flows whose initial points belong to small cells other than the grand cell and preserving small cells. To obtain such flows, we consider the cell decomposition of the grand cell induced by Bruhat decomposition of the flag variety. We show that such full Kostant-Toda flow can be reduced to the ordinary tridiagonal Toda flow by using sheaf theoretical methods.

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KW - Full Kostant-Toda lattice

KW - Gauss decomposition

KW - Kazhdan's x-grading

KW - Toda lattice

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