[1] |
M. Adler; M. Adler · Zbl 0414.58020 |
[2] |
Auslander, L.; Kostant, B., Polarization and unitary representations of solvable Lie groups, Invent. Math., 14, 255-354 (1971) · Zbl 0233.22005 |
[3] |
Bogoyavlensky, O. I., On perturbations of the periodic Toda lattice, Comm. Math. Phys., 51, 201-209 (1976) |
[4] |
Dixmier, J., Algèbres enveloppantes, (Cahiers scientifiques no. 27 (1974), Gauthier-Villars: Gauthier-Villars Paris) · Zbl 0422.17003 |
[5] |
Dynkin, E. B., The structure of semi-simple Lie algebras, Amer. Math. Soc. Transl. Ser., 1, No. 17 (1950) · Zbl 0052.26202 |
[6] |
Dynkin, E. B., Semi-simple subalgebras of semi-simple Lie algebras, Amer. Math. Soc. Transl. Ser. 2, 6, 111-244 (1957) · Zbl 0077.03404 |
[7] |
Dynkin, E. B., The maximal subgroups of the classical groups, Amer. Math. Soc. Transl. Ser. 2, 6, 245-378 (1957) · Zbl 0077.03403 |
[8] |
Flaschka, H., On the Toda lattice, II, Progr. Theor. Phys., 51, 703-716 (1974) · Zbl 0942.37505 |
[9] |
Gelfand, I. M.; Kazhdan, D. A., Representations of the group \(Gl (n, K)\) where \(K\) is a local field, (Lie Groups and Their Representations (1975), Wiley: Wiley New York), 95-118 · Zbl 0348.22011 |
[10] |
R. Hermann; R. Hermann · Zbl 0381.35001 |
[11] |
Humphreys, J., Introduction to Lie Algebras and Representation Theory, (Graduate Texts in Mathematics No. 9 (1972), Springer-Verlag: Springer-Verlag New York/Berlin) · Zbl 0254.17004 |
[12] |
Kostant, B., The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math., 81, 973-1032 (1959) · Zbl 0099.25603 |
[13] |
Kostant, B., Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math., 74, 329-387 (1961) · Zbl 0134.03501 |
[14] |
Kostant, B., Lie group representations on polynomial rings, Amer. J. Math., 85, 327-404 (1963) · Zbl 0124.26802 |
[15] |
Kostant, B., Quantization and unitary representations, (Lecture Notes in Mathematics No. 170 (1970), Springer-Verlag: Springer-Verlag New York/Berlin), 87-208 · Zbl 0223.53028 |
[16] |
Kostant, B., On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Normale Supérieure, 6, 413-455 (1973) · Zbl 0293.22019 |
[17] |
Kostant, B., On Whittaker vectors and representation theory, Invent. Math., 48, 101-184 (1978) · Zbl 0405.22013 |
[18] |
Kostant, B.; Rallis, S., Orbits and representations associated with symmetric spaces, Amer. J. Math., 93, 753-809 (1971) · Zbl 0224.22013 |
[19] |
Moser, J., Finitely many mass points on the line under the influence of an exponential potential—an integrable system, (Battelle Rencontres Summer Lectures. Battelle Rencontres Summer Lectures, Lecture Notes in Mathematics (1974), Springer-Verlag: Springer-Verlag New York/Berlin), 467-487 · Zbl 0323.70012 |
[20] |
Olshanetzki, M. A.; Perelomov, A. M., Completely integrable Hamiltonian systems connected with semi-simple Lie algebras, Invent. Math., 37, 93-108 (1976) · Zbl 0342.58017 |
[21] |
Pukanszky, L., On the theory of exponential groups, Trans. Amer. Math. Soc., 126, 487-507 (1967) · Zbl 0207.33605 |
[22] |
Shafarevich, I. R., Basic Algebraic Geometry (1977), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0362.14001 |
[23] |
Suguira, M., Conjugate classes of Cartan subalgebras in real semi-simple Lie algebras, J. Math. Soc. Japan, 11, 374-434 (1959) · Zbl 0204.04201 |
[24] |
Toda, M., Studies of a non-linear lattice, Phys. Rep. C, Phys. Lett., 8, 1-125 (1975) |
[25] |
van Moerbeke, P., The spectrum of Jacobi matrices, Invent. Math., 37, 45-81 (1976) · Zbl 0361.15010 |
[26] |
Varadarajan, V. S., Lie Groups, Lie Algebras and Their Representations (1974), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0371.22001 |
[27] |
Adler, M., On a trace functional for formal pseudodifferential operators and the symplectic structure for the Korteweg-de Vries type equations, Invent. Math., 50, 219-248 (1979) · Zbl 0393.35058 |
[28] |
Olshanetzki, M. A.; Perelomov, M. A., Explicit solution of the classical generalized Toda models (1978), preprint |
[29] |
Leznov, A. N.; Saveliev, M. V., Representation of zero curvature for the system of nonlinear partial differential equations \(xa,zz̄ = exp(kx)a\) and its integrability (1979), Serpurchev, USSR · Zbl 0415.35017 |