Limit matrices for the Toda flow and periodic flags for loop groups

M. Adler; L. Haine; P. van Moerbeke

doi:10.1007/bf01445092

journal article Dec 01, 1993

Limit matrices for the Toda flow and periodic flags for loop groups

M. Adler L. Haine P. van Moerbeke

Mathematische Annalen Vol. 296 No. 1 pp. 1-33 · Springer Science and Business Media LLC

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References

21

[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) 10.1007/bf01947073

[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) 10.1016/0001-8708(80)90007-9

[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 10.1016/b978-0-12-400465-8.50020-1

[6]

Flaschka, H., Haine, L.: Variet�s de drapeaux et r�seaux de Toda. Math. Z.208, 545?556 (1991) 10.1007/bf02571544

[7]

Goodman, R., Wallach, N.: Classical and quantum mechanical systems of Toda-lattice type. Commun. Math. Phys.94, 177?217 (1984) 10.1007/bf01209301

[8]

Kac, V.G.: Infinite dimensional Lie algebras 3rd ed. Cambridge: Cambridge Univ. Press 1990 10.1017/cbo9780511626234

[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) 10.1016/0001-8708(79)90057-4

[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) 10.1007/bf01391179

[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) 10.1007/bf01389063

[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) 10.1007/bf02698802

[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) 10.1007/bf02392090

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Published: Dec 01, 1993
Vol/Issue: 296(1)
Pages: 1-33
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M. Adler, L. Haine, P. van Moerbeke (1993). Limit matrices for the Toda flow and periodic flags for loop groups. Mathematische Annalen, 296(1), 1-33. https://doi.org/10.1007/bf01445092

Limit matrices for the Toda flow and periodic flags for loop groups

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