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Limit Matrices for the Toda Flow and Periodic Flags for Loop-groups

Bibliographic reference Adler, M. ; Haine, Luc ; Van Moerbeke, Pierre. Limit Matrices for the Toda Flow and Periodic Flags for Loop-groups. In: Mathematische Annalen, Vol. 296, no. 1, p. 1-33 (1993)
Permanent URL http://hdl.handle.net/2078.1/49698
  1. Adler, M., van Moerbeke, P.: Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization. Commun. Math. Phys.83, 83?106 (1982); The Toda lattice, Dynkin diagrams, singularities and Abelian varieties. Invent. Math.103, 223?278 (1991)
  2. Adler, M., van Moerbeke, P.: Birkhoff strata, B�cklund transformations and limits of isospectral operators. Adv. Math. (1993)
  3. Adler, M., van Moerbeke, P.: Completely integrable systems, Euclidean Lie algebras and curves; Linearization of Hamiltonian systems, Jacobi varieties and representation theory. Adv. Math.38, 267?317; 318?379 (1980)
  4. Date, E., Jimbo, M., Kashiwara, M., Miwa, T.: Transformation groups for soliton equations. Proceedings of RIMS Symposium on Non Linear Integrable Systems-Classical and Quantum Theory, pp 39?119, Kyoto 1981. In: Jimbo, M., Miwa, T., (eds.), Singapore World Scientific 1983
  5. Flaschka, H.: The Toda lattice in the complex domain. In: Algebraic analysis, vol. 1, pp. 141?154. London New York Academic Press 1988
  6. Flaschka, H., Haine, L.: Variet�s de drapeaux et r�seaux de Toda. Math. Z.208, 545?556 (1991)
  7. Goodman, R., Wallach, N.: Classical and quantum mechanical systems of Toda-lattice type. Commun. Math. Phys.94, 177?217 (1984)
  8. Kac, V.G.: Infinite dimensional Lie algebras 3rd ed. Cambridge: Cambridge Univ. Press 1990
  9. Kac, V.G., Peterson, D.H.: Lectures on the infinite wedge-representation and the MKP-hierarchy. Syst�mes dynamiques non lin�aires S�min. Math. Sup�r.102, Presses Univ. de Montr�al (1986)
  10. Kostant, B.: The solution to a generalized Toda lattice and representation theory. Adv. Math.34, 195?338 (1979)
  11. Mumford, D.: Tata lectures on theta II. Boston Basel Stuttgart: Birkh�user 1984
  12. Pressley, A., Segal, G.: Loop groups. Oxford: Clarendon Press 1986
  13. Reiman, A.G., Semenov-Tjan-Shanskii, M.A.: Reduction of Hamiltonian systems, affine Lie algebras and Lax equations I. Invent. Math.54, 81?100 (1979)
  14. Reiman, A.G., Semenov-Tjan-Shanskii, M.A.: Reduction of Hamiltonian systems, affine Lie algebras and Lax equations II. Invent. Math.63, 423?432 (1981)
  15. Sato, M.: Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds. RIMS Kokyuroku439, 30?46 (1981)
  16. Sato, M.: Soliton equations and the universal Grassmann manifold (by Noumi, in Japanese). Math. Lect. Notes 18, Sophia University 1984
  17. Sato, M., Sato, Y.: Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds. Lect. Notes Num. Appl. Anal.5, 259?271 (1982)
  18. Segal, G., Wilson, G.: Loop groups and equations of KdV type. Publ. Math. Inst. Hautes �tud. Sci.61, 5?65 (1985)
  19. Ueno K., Takasaki K.: Toda lattice hierarchy. In: Advanced Studies in Pure Math. 4, Group representations and systems of differential equations, pp. 1?95 (1984)
  20. van Moerbeke, P.: The isospectral deformations of discrete Laplacians. Springer Verlag Lecture Notes755, 313?370 (1979); and: The spectrum of Jacobi matrices. Invent. Math.37, 45?81 (1976)
  21. van Moerbeke, P., Mumford, D.: The spectrum of difference operators and algebraic curves. Acta Math.143, 93?154 (1979)