G_2型2-Toroidal李代数的顶点表示

Vertex Representation of 2-Toroidal Lie Algebra of Type G_2

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 [-47. [-5], the authors gave the vertex representations of the simplylaced toroidal Lie algebra, and according to the above, [-6] gave the construction of the vertex representation of toroidal Lie Algebra T （BD. According to the main idea of [-6], we give the construction of the vertex representation of the toroidal Lie algebra T（G2）. This construction has the dose relation with the Dynkin diagram of type D4 and a 2-cocycle.