Transformation Groups for Soliton Equations —Euclidean Lie Algebras and Reduction of the KP Hierarchy—
Transformation Groups for Soliton Equations —Euclidean Lie Algebras and Reduction of the KP Hierarchy—
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DOI：
10.2977/prims/1195183297
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发表时间：
1982-12
影响因子：
1.2
通讯作者：
E. Date;M. Jimbo;M. Kashiwara;T. Miwa
中科院分区：
文献类型：
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作者：
E. Date;M. Jimbo;M. Kashiwara;T. Miwa
这是我们关于孤子方程变换群的系列论文[1]、[3]、[10]、[11]的最后一章。文献[1]中发现了KdV(Korteweg De Vries)方程与仿射李代数A之间的联系：显式实现A{[2]的基本表示的顶点算子作用于KdV族的i个函数。KdV方程和A[之间的这种联系来自于Kp(Kadomtsev-Petviashvili)方程和gl(Oo)之间的类似联系；对gl(Oo)中子代数A{^的限制将Kp系归结为KdV系.
This is the last chapter of our series of papers [1], [3], [10], [11] on transformation groups for soliton equations. In [1] a link between the KdV (Korteweg de Vries) equation and the affine Lie algebra A[^ was found: the vertex operator that affords an explicit realization of the basic representation of A{ [2] acts infinitesimally on the i functions of the KdV hierarchy. It was shown also that this link between the KdV equation and A[ comes from a similar link between the KP (Kadomtsev-Petviashvili) equation and gl(oo); the restriction to the subalgebra A{^ in gl(oo) reduces the KP hierarchy to the KdV hierarchy.