Variétés de drapeaux et réseaux de Toda. (Flag manifolds and Toda lattices). (French) Zbl 0744.58031
For the review see C. R. Acad. Sci., Paris, Sér. I 312, No. 3, 255-258 (1991; Zbl 0721.58021).
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 17B20 | Simple, semisimple, reductive (super)algebras |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
References:
| [1] | Adler, M., van Moerbeke, P.: The Toda lattice, Dynkin diagrams, singularities and Abelian varieties. Invent. Math.103, 223–278 (1991) · Zbl 0735.14031 · doi:10.1007/BF01239513 |
| [2] | Bernstein, I.N., Gel’fand, I.M., Gel’fand, S.I.: Schubert cells and cohomology of the spaces G/P. Russ. Math. Surv.28, 1–26 (1973) · Zbl 0289.57024 · doi:10.1070/RM1973v028n03ABEH001557 |
| [3] | Bremner, M.R., Moody, R.V., Patera, J.: Tables of dominant weight multiplicities for representations of simple Lie algebras. New York: Marcel Dekker 1985 · Zbl 0557.17001 |
| [4] | Deift, P.A., Li, L.C., Nanda, T., Tomei, C.: The Toda flow on a generic orbit is integrable. Commun. Pure Appl. Math.39, 183–232 (1986) · Zbl 0606.58020 · doi:10.1002/cpa.3160390203 |
| [5] | Ercolani, N.M., Flaschka, H., Haine, L.: Painlevé balances and dressing transformations. (Preprint) · Zbl 0856.34011 |
| [6] | Flaschka, H.: The Toda lattice in the complex domain. In: Kashiwara, M., Kawai, T. (eds.) Algebraic Analysis, vol. 1, pp. 141–154. Boston, Mass.: Academic Press 1988 |
| [7] | Flaschka, H., Haine, L.: Torus orbits in G/P. Pacific J. Math.149, 251–292 (1991) · Zbl 0788.22017 |
| [8] | Flaschka, H., Zeng, Y.: Painlevé analysis for the semisimple Toda lattice. (Preprint) |
| [9] | Gel’fand, I.M., Serganova, V.V.: Combinatorial geometries and torus strata on homogeneous compact manifolds. Russ. Math. Surv.42, 133–168 (1987) · Zbl 0639.14031 · doi:10.1070/RM1987v042n02ABEH001308 |
| [10] | Goodman, R., Wallach, N.R.: Classical and quantum mechanical systems of Toda lattice type, II. Solutions of the classical flows. Commun. Math. Phys.94, 177–217 (1984) · Zbl 0592.58028 · doi:10.1007/BF01209301 |
| [11] | Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Am. J. Math.81, 973–1032 (1959) · Zbl 0099.25603 · doi:10.2307/2372999 |
| [12] | Kostant, B.: Lie group representations on polynomial rings. Am. J. Math.85, 327–404 (1963) · Zbl 0124.26802 · doi:10.2307/2373130 |
| [13] | Kostant, B.: On Whittaker vectors and representation theory. Invent. Math.48, 101–184 (1978) · Zbl 0405.22013 · doi:10.1007/BF01390249 |
| [14] | Kostant, B.: The solution to a generalized Toda lattice and representation theory. Adv. Math.34, 195–338 (1979) · Zbl 0433.22008 · doi:10.1016/0001-8708(79)90057-4 |
| [15] | Ol’shanetskyi, M.A., Perelomov, A.M.: Explicit solutions of the classical generalized Toda models. Invent. Math.54, 261–269 (1979) · Zbl 0419.58008 · doi:10.1007/BF01390233 |
| [16] | Reyman, A.G.: Integrable systems connected with graded Lie algebras. J. Sov. Math.19, 1507–1545 (1982) · Zbl 0554.70010 · doi:10.1007/BF01091461 |
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