关键词: 既约包络代数, 极大向量, 特征标, 极小左理想, 不可约模

Abstract:

In this paper,  the authors study the irreducible modules by determining the maximal weight vector which generates the minimal left ideal of the reduced enveloping algebra. They obtain a complete set of non-isomorphic irreducible modules for Special algebra $S(3, {\bf 1})$ when the height of the characters is not larger than 0 and characteristic of the field is 2, and determine their dimension.

Key words: Maximal weight vector, Character, Minimal left ideal, Irreducible module