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Ikeda, Kaoru

Compactifications of the iso level sets of the Hessenberg matrices and the full Kostant-Toda lattice. (English) Zbl 1130.37385

Proc. Japan Acad., Ser. A 82, No. 7, 93-96 (2006).
Summary: We consider the problem of the compactification of the iso level sets of the Hessenberg matrices which is propounded by N. M. Ercolani, H. Flaschka and S. Singer [in: Integrable systems: the Verdier memorial conference, France, July 1–5, 1991, Boston, MA, Birkhäuser, Prog. Math. 115, 181–225 (1993; Zbl 0819.58014)]. We determine the structure of the cohomology ring of the compact iso level set and obtain a new expression of the flag variety \(G/B\).

Cited in 2 Documents

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests

Keywords:

full Kostant-Toda lattice; Gauss decomposition; iso level set; flag manifold

Citations:

Zbl 0819.58014
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\textit{K. Ikeda}, Proc. Japan Acad., Ser. A 82, No. 7, 93--96 (2006; Zbl 1130.37385)
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References:

[1] N. Ercolani, H. Flaschka and S. Singer, The geometry of the full Kostant-Toda lattice, in Integrable systems ( Luminy , 1991) 181-225, Prog. Math., 115, Birkhäuser, Boston, 1993. · Zbl 0819.58014
[2] H. Flaschka and L. Haine, variétés de drapeaux et réseaux de Toda, Math. Z. 208 (1991), 545-556. · Zbl 0744.58031
[3] Y. Guivarc’h, L. Ji and J. Taylor, Compactifications of symmetric spaces , Prog. Math., 156, Birkhäuser Boston, Boston, 1998.
[4] K. Ikeda, The full Kostant-Toda flow associated with the small cell of the flag variety. (Preprint). · Zbl 0793.20011
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