TY - JOUR
T1 - The Toda flows preserving small cells of the flag variety G / B and Kazhdan's x0-grading
AU - Ikeda, Kaoru
N1 - 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.
PY - 2007/2
Y1 - 2007/2
N2 - 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.
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.
KW - Bruhat decomposition
KW - Full Kostant-Toda lattice
KW - Gauss decomposition
KW - Kazhdan's x-grading
KW - Toda lattice
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U2 - 10.1016/j.geomphys.2006.06.003
DO - 10.1016/j.geomphys.2006.06.003
M3 - Article
AN - SCOPUS:33751203843
VL - 57
SP - 799
EP - 813
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
SN - 0393-0440
IS - 3
ER -