Is the paper [2] the authors defined the singular Darboux transformations and established an explicit formula for constructing unitons from a simply connected Riemann surface. M to the group U(N). The formula is obtai...Is the paper [2] the authors defined the singular Darboux transformations and established an explicit formula for constructing unitons from a simply connected Riemann surface. M to the group U(N). The formula is obtained as a limit of an infinite consequence of Darboux transformations through some renormalization procedure. In the present paper the authors give a complete proof of the fact that the formula gives a global solution of harmonic maps without singularity.展开更多
For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a sy...For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set M which depends only on the root category R and prove that there is a bijection between M and ˙B, where R is the T^2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U^+.展开更多
基金he Special Funds for Major State Basic Ressarch Project of China (NonlinearScience), the National Natural Science Foundation o
文摘Is the paper [2] the authors defined the singular Darboux transformations and established an explicit formula for constructing unitons from a simply connected Riemann surface. M to the group U(N). The formula is obtained as a limit of an infinite consequence of Darboux transformations through some renormalization procedure. In the present paper the authors give a complete proof of the fact that the formula gives a global solution of harmonic maps without singularity.
基金supported by the Fundamental Research Funds for the Central Universities(No.BLX2013014)the National Natural Science Foundation of China(No.11131001)
文摘For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set M which depends only on the root category R and prove that there is a bijection between M and ˙B, where R is the T^2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U^+.
