Abstract
We present a unified method for constructing generalized flag transformations of unitons into a Lie groupG via singular Darboux transformations. These flag transformations provide the possibility to establish some factorizations forG-unitons.
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References
Uhlenbeck, K., Harmonic maps into Lie groups (Classical solutions of the chiral model), J. Diff. Geom., 1989, 30: 1–50.
Segal, G. B., Loop Groups and Harmonic Maps, Advances in Homotopy Theory, L.M.S. Lecture Notes, 139, Cambridge: Cambridge Univ. Press, 1989, 153–164.
Wood, J. C., Explicit construction and parametrization of harmonic two-spheres in the unitary group, Proc. London Math. Soc., 1989, 59: 608–624.
Guest, M. A., Ohnita, Y., Group actions and deformations for harmonic maps, J. Math. Soc. Japan, 1993, 45(4): 671–704.
Anand, C. K., A closed form for Unitons, J. Math. Soc. Japan, 1998, 50(3): 737–751.
Gu, C. H., Hu, H. S., Explicit construction of harmonic maps fromR 2 toU(N), Chin. Ann. of Math., 1995, 16B, 1–6.
Gu, C. H., Hu, H. S., Constructions of unitons via purely algebraic algorithm, Chin. Ann. of Math., 1999, 20B, 1–6.
Burstall, F. E., Guest, M. A., Harmonic two-spheres in compact symmetric spaces, revisited, Math. Ann., 1997, 309: 541–572.
Gu, C. H., Hu, H. S., Some remarks on singular Darboux transformations for unitons, Chin. Ann. of Math., 2001, B 22(3): 263–266.
Gu, C. H., Dong, Y. X., Shen, Y. B., Constructive factorizations of unitons via singular Darboux transformation, Science in China, Ser. A, 2000, 43(2): 149–157.
Gu, C. H., Unitons of harmonic maps fromR 2 toU(p,q), Letters in Math. Phys., 1998, 46: 347–357.
He, Q., Shen, Y. B., The factorization and symplectic uniton numbers for harmonic maps into symplectic group, Science in China, Ser. A, 2001, 31(11): 973–982.
Burstall, F. E., Rawnsley, J. H., Twistor Theory for Riemannian Symmetric Spaces, Lectrure Notes in Math. 1424, Berlin: Springer-Verlag, 1990.
Valli, G., On the energy spectrum of harmonic 2-spheres in unitary groups, Topology, 1988, 27: 129–136.
Sacks, J., Uhlenbeck, K., The existence of minimal immersions of 2-spheres, Ann. of Math., 1981, 113: 1–24.
Koszul, J. L., Malgrange, B., Sur certaines structures fibres complexes, Arch. Math., 1958, 9: 102–109.
Burstall, F. E., Wood, J. C., The construction of harmonic maps into complex Grassmannians, J. Diff. Geom., 1986, 23: 255–297.
Dong, Y. X., On energy gap of unitons, Math. Z., to appear.
Guest, M., Harmonic Maps, Loop Groups, and Integrable Systems, Cambridge: Cambridge University Press, 1997.
Dong, Y. X., On harmonic maps from surfaces into Lie groups via Bruhat decomposition, to appear.
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Yuxin, D. On Darboux and singular Darboux transformations ofG-unitons. Sci. China Ser. A-Math. 45, 1497–1505 (2002). https://doi.org/10.1360/02ys9161
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DOI: https://doi.org/10.1360/02ys9161