There are two parts in this article . part i is mainly discussing an elementary problem in kac - moody algebra : how to describe the real and imaginary root vectors corresponding to a given real or imaginary root 本文分为两个相对独立的篇章：第一部分主要讨论了kac - moody代数中的一类基本问题，即给定一个实根或虚根，其对应的实根向量和虚根向量该如何表示
