sl(2,F)作用在有限维空间上所对应矩阵的秩

The Ranks of the Matrices with Respect to sl(2,F)Acting on a Finite Dimensional Vector Spaces

主要研究特殊线性李代数L=sl(2,F)中的任意一个元作用在有限维向量空间V(dimV=m+1)的一组基上的不可约表示所对应矩阵的秩.依次对ax+by+ch∈L中a,b,c有两个为零、一个为零、均不为零的情形进行讨论,得出更一般情形中矩阵秩的情况.

This paper studies the role of any one element in L=sl（2,F）which acts on the basis of finite-dimensional vector space,its matrix corresponds to the rank of irreducible representation,and sequentially to a,b,c of ax＋by＋ch∈Lthat have two zero（Lemma 1）,a zero（Lemma 2）,not zero（Lemma 3）in the situation,resulting in the case of the general case of matrix rank.