单李代数不可约表示的标记

THE LABEL OF THE IRREDUCIBLE REPRESENTATION FOR ANY SIMPLE LIE ALGEBRA

对于n秩单李代数g,当采用Dynkin关于素根的分类时,其不可约表示可以用n个非负整数Aai标记,也可通过初等表示的权用数组li来标记。刊用Cartan逆矩阵,我们给出了计算Aa_i与li之间关系的方法。对于B_n、C_n、D_n和F_4利用Cartan逆矩阵证明了这些li是与采用Cartan关于素根的分类时的Ai是一致的。

For simple Lie algebrag of rankn, when the Dynkin Classification ofsimple roots is chosen, its irreducible representation can be labelled by nunnegative integers (?)α_i and also be labelled by li by using the weightsof elementary representation. By means of the Cartan inverse matrix, themethods for calculating the relationsbetween (?)α_i and li are given. Theseli and (?)_i for which the Cartan classification of simple roots is chosen areidentified for B_n, C_n, D_n, and F_4.