对称群的特征标与一个行列式问题

提供了用对称群特征标的明显表示式，求出在实分析以及有限群表示论中均有的一个多变化元行列式的两个表示式，并运用对称群特征标的线性表示定理导出了该多变元行列式的一个递推关系式。

Group characters of symmetric groups and a determinantal problem

This paper presents an explicit expansion of the determinant that will play an important role in the real analysis and the group representations by using the explicit expressions of the group characters of the symmetric groups,and gives also a recursion formula on this determinant by using the linear representation theorem on the character of the symmetric group.