G_2型2-Toroidal李代数的顶点表示

Abstract

在[4]和[5]中已经研究了sim p ly-laced型T oro idal李代数的顶点表示,[6]文据此给出了Bl型T oro idal李代数顶点表示的构造.受[6]文启发,本文给出了G2型T oro idal李代数的顶点表示的构造,这种构造方式与D(41)的D ynk in图的顶点粘合和一个2上循环有着紧密联系.

In ,the authors gave the vertex representations of the simplylaced toroidal Lie algebra,and according to the above, gave the construction of the vertex representation of toroidal Lie Algebra T(B_l).According to the main idea of [6],we give the construction of the vertex representation of the toroidal Lie algebra T(G_2).This construction has the close relation with the Dynkin diagram of type D~((1))_4 and a 2-cocycle.