@article{SEDP_1990-1991____A8_0, author = {Takasaki, Kanehisa}, title = {Hidden symmetries of integrable systems in {Yang-Mills} theory and {K\"ahler} geometry}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:8}, pages = {1--15}, publisher = {Ecole Polytechnique, Centre de Math\'ematiques}, year = {1990-1991}, mrnumber = {1131581}, zbl = {0746.58039}, language = {en}, url = {http://www.numdam.org/item/SEDP_1990-1991____A8_0/} }
TY - JOUR AU - Takasaki, Kanehisa TI - Hidden symmetries of integrable systems in Yang-Mills theory and Kähler geometry JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:8 PY - 1990-1991 SP - 1 EP - 15 PB - Ecole Polytechnique, Centre de Mathématiques UR - http://www.numdam.org/item/SEDP_1990-1991____A8_0/ LA - en ID - SEDP_1990-1991____A8_0 ER -
%0 Journal Article %A Takasaki, Kanehisa %T Hidden symmetries of integrable systems in Yang-Mills theory and Kähler geometry %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:8 %D 1990-1991 %P 1-15 %I Ecole Polytechnique, Centre de Mathématiques %U http://www.numdam.org/item/SEDP_1990-1991____A8_0/ %G en %F SEDP_1990-1991____A8_0
Takasaki, Kanehisa. Hidden symmetries of integrable systems in Yang-Mills theory and Kähler geometry. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1990-1991), Exposé no. 8, 15 p. http://www.numdam.org/item/SEDP_1990-1991____A8_0/
[Sa-Sa] Soliton equations as dynamical systems in an infinite dimensional Grassmann manifold, in Nonlinear Partial Differential Equations in Applied Sciences, P.D. Lax, H. Fujita, G. Strang (eds.), North-Holland, 1982 | Zbl
, ,[Se-Wi] Loop groups and equations of KdV type, Publ. IHES 61 (1985), 5-65. | Numdam | MR | Zbl
, and ,[Ta1] Geometry of universal Grassmannian manifold from algebraic point of view, Reviews in Math. Phys. 1 (1989), 1-46. | MR | Zbl
,[Ch] Chiral fields, self-dual Yang-Mills fields as integrable systems, and the role of the Kac-Moody algebra, in Nonlinear phenomena, K.B. Wolf (ed.), Lecture Notes in Physics vol. 189, Splinger-Verlag, 1983. | MR | Zbl
,[Bo] The geometry of self-dual Einstein spaces, in Nonlinear Phenomena, K.B. Wolf (ed.), Lecture Notes in Physics vol. 189, Springer, 1983. | MR
,[Wal] On self-dual gauge fields, Phys. Lett. 61A (1977), 81-82. | MR | Zbl
,[Pe] Nonlinear gravitons and curved twistor theory, Gen. Rel. Grav. 7 (1976), 31-52. | MR | Zbl
,[Be-Za] Yang-Mills equations as inverse scattering problem, Phys. Lett. 73B (1978), 53-57. | MR
and ,[Ch-Pr-Si] Some aspects of the linear system for self-dual Yang-Mills fields, Phys. Rev. D24 (1981), 1574-1580. | MR
, and ,[Fo-Ho-Pa] Towards complete integrability of the self-dual equations, Phys. Rev. D23 (1981), 1876- . | MR
, , and ,[Po] On the Lagrangian theory of anti-self-dual fields in four dimensional Euclidean space, Commun. Math. Phys. 72 (1980), 37-47. | MR
,[Wa2] Completely solvable gauge-field equations in dimension greater than four, Nucl. Phys. B236 (1984), 381-396. | MR
,[Co-Go-Ke] Some comments on the ADHM construction in 4k dimensions, Commun. Math. Phys. 100 (1985), 1-13. | MR | Zbl
, , and ,[At-Hi-Dr-Ma] Construction of instantons, Phys. Lett. 65A (1978), 185-187; , Geometry of gauge fields, Scuola Norm. Sup., Pisa, 1979. | MR | Zbl
, , and ,[Ya] Condition of self-duality for SU(2) gauge fields on Euclidean four-dimensional space, Phys. Rev. Lett. 38 (1977), 1377-1379. | MR
,[P1] Some solutions of complex Einstein equations, J. Math. Phys. 16 (1975), 2395-2402. | MR
,[Hi-Ka-Li-Ro] Hyperkähler metrics and supersymmetry, Commun. Math. Phys. 108 (1987), 535-589. | MR | Zbl
, , , and ,[Tw1] Lerner, D.E., and Sommers, P.D. (ed.), Complex manifold techniques in theoretial physics, Pitman, 1978. | Zbl
[Tw2] Hughston, L.P., and Ward, R.S. (ed.), Advances in twistor theory, Pitman, 1979. | MR | Zbl
[Tw3] Doebner, H.D., and Palev, T.D. (ed.), Twistor geometry and non-linear systems, Lecture Notes in Mathematics vol. 970, Springer-Verlag, 1982. | MR | Zbl
[Tw4] Twistor geometry and field theory, Cambridge University Press, 1989. | MR | Zbl
, and ,[Tw5] Mason, L.J., and hughston, L.P. (ed.), Further advances in twistor theory, Pitman, 1990.
[Tw6] Baily, T.N., and Boston, R.J. (ed.), Twistors in mathematics and physics, London Mathematical Society Lecture Note Series vol. 156, Cambridge University Press, 1990. | MR | Zbl
[Ka] Infinite dimensional Lie algebras, Cambridge Univ. Press, 1985. | MR | Zbl
,[Pr-Se] Loop groups and their representations, Oxford University Press, 1986. | MR | Zbl
, and ,[Da-Ji-Mi-Ka] Transformation theory for soliton equations III-VI, J. Phys. Soc. Japan 50 (1982), 3806-3812, 3813-3818; Phyica 4D (1982), 343-365; Publ. RIMS., Kyoto Univ., 18 (1982), 1077-1110.
, , , ,[Ue-Na] Transformation theory for anti-self-dual equations and the Riemann-Hilbert problem, Phys. Lett. 109B (1982), 273-278. | MR
, ,(Ch-Ge-WuJ Kac-Moody algebra in the self-dual Yang-Mills equation, Phys. Rev. D25 (1982), 1086-1094. | MR
, , ,[Do] A new symmetry group of real self-dual Yang-Mills theory, Phys. Lett. 113B (1982), 387-390. | MR
,[Bo-P1] An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces, J. Math. Phys. 26 (1985), 229-234. | MR | Zbl
, ,[Ta2] A new approach to the self-dual Yang-Mills equations, Commun. Math. Phys. 94 (1984), 35-59; Hierarchy structure in integrable systems of gauge fields and underlying Lie algebras, Commun. Math. Phys. 127 (1990), 225-238. | MR | Zbl
,[Ta3] An infinite number of hidden variables in hyper-Kähler metrics, J. Math. Phys. 30 (1989),1515-1521; Symmetries of hyper-Kähler (or Poisson gauge field) hierarchy, J. Math. Phys. 31 (1990), 1877-1888. | MR | Zbl
,[Le-Mu] Deformation of algebras and solutions of self-duality equation, J. Math. Phys. 28 (1987), 2574-2578. | MR | Zbl
, ,[Le-Sa] Exactly and completely integrable nonlinear dynamical sysmtems, Acta Applicandae Mathematicae 16 (1989), 1-74. | MR | Zbl
, ,[Ta4] Integrable systems in gauge theory, Kähler geometry and super KP hierarchy - symmetries and algebraic point of view, talk at ICM-90, Kyoto, August, 1990; Kyoto University preprint RIMS-714, September, 1990. | MR
,[Bi-F1-Sa] The self-dual closed membranes, Phys. Lett. 198B (1987), 329-332. | MR
, , and ,[F1-Le] Integrability of the self-dual membranes in (4+1) dimensions and the Toda lattice, Phys. Lett. 223B (1989), 153-156. | MR
, and ,[Gr-Tz] Generalized self-dual bosonic membranes, vector corss-products and analyticity in higher dimensions, Phys. Lett. 224B (1989), 259-264. | MR
, and ,[Za] Self-duality in the theory of the bosonic p-branes, Phys. Lett. 211B (1988), 281-284. | MR
,[Ar-Sa] Cocycles of area-preserving diffeomorphisms and anomalies in the theory of relativistic surfaces, Phys. Lett. 214B (1988), 350-356. | MR
, and ,[Ba-Po-Se] Central extensions of area preserving membrane algebras, Phys. Lett. 210B (1988), 85-91. | MR
, , and ,[F1-I1] Iliopoulos, A note on the classical symmetries of the closed bosonic membranes, J., Phys. Lett. 201B (1988), 237-240. | MR
, and[Ho1] DiffAT2, and the curvature of some infinite dimensional manifolds, Phys. Lett. 215B (1988), 706-710. | MR
,[Ho2] Diffeomorphism groups, quantization, and SU(oo), Int. J. Mod. Phys. A 4 (19) (1989), 5235-5248. | MR | Zbl
,[Ba1] The large-N limit of extended conformal symmetries, Phys. Lett. 228B (1989), 57-63. | MR
,[Ba2] The structure of the W∞ algebra, Maryland University preprint UMD-90-085, November, 1980.
,[Oo-Va] Self-duality and N = 2 string magic, Univ. Chicago preprint, EFI-90-24, April 1990. | MR | Zbl
, and ,[Ya-Ch] Induced 4d self-dual quantum gravity:- W∞ algebraic approach -, Laurence Livermore National Laboratory preprint, April 1990. | Zbl
, and ,[Pa1] Self-dual gravity as a large-N limit of the 2D non-linear sigma model, Phys. Lett. 238B (1990), 287-290. | MR
,[Pa2] Extended conformal symmetries in real heavens, Phys. Lett. 236B (1990), 429-432. | MR
,[Wi] Surprises with topological field theorries, Advanced Study Institute preprint IASSNS-HEP-90/37, April, 1990.
,[Bo-Fi] Killing vectors in self-dual, Euclidean Einstein spaces, J. Math. Phys. 23 (1982), 1126-1128. | MR | Zbl
, and ,[Ge-Da] Stationary Riemannian space-times with self-dual curvature, Gen. Rel. Grav. 16 (1984), 817-829. | MR | Zbl
, and ,[Hi] Complex manifolds and Einstein's equations, in Twistor Geometry and Non-linear Systems, H.D. Doebner and T. Weber (eds.), Lecture Notes in Mathematics vol. 970, pp.2-42, Springer-Verlag 1982. | MR | Zbl
,[Jo-To] Minitwistor spaces and Einstein-Weyl spaces, Class. Quantum Grav. 2 (1985), 565-577. | MR | Zbl
, and ,[Wa3] Winstein-Weyl spaces and SU(∞) Toda fields, Class. Quantum Grav. 7 (1990). L95-L98. | Zbl
,[LeBr] Explicit self-dual metrics on CP2 # ... # CP2, preprint, 1990.
,[Sa-Ve] Continual analogues of contragredient Lie algebras, Commun. Math. Phys. 126 (1989), 367-378; New examples of continuum graded Lie algebras, Phys. Lett. 143A (1990), 121-128. | MR | Zbl
, and ,