摘要
人们知道 SU(2 ) 的不可约酉表示的矩阵元是相互正交且平方可积的 (Peter- Weyl定理 ) .对于 SL (2 ,R)的主级数表示和离散级数表示的矩阵系数是否有类似的结果 ?在该文中 ,作者部分给出了这个问题的肯定回答 ,即关于主级数表示的矩阵系数是准平方可积的 ,关于离散级数表示的矩阵系数是平方可积的 .此外 ,他们还得到了离散级数表示 (除 n=± 1外 )在子空间 ′n上的矩阵系数是绝对可积的 .
It is well known that the matrical elements of i rreducible unitary representations of SU(2) are mutually orthogonal and square integrable (Pet er-Weyl theorem). We want to see if the similar results for the matrix coeffici ents of the principal series and the discrete series representations of SL(2,R ) are true. In this paper, an answer of this problem is given partially, i.e. the matrix coefficients of the principal series representations are pre-square integrable, and that of the discrete series representations are square integrabl e. In addition, the matrix coefficients of the discrete series representations ( except for n=±1) on the subspace ′ n are absolutely integrable.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2002年第1期77-82,共6页
Acta Mathematica Scientia
关键词
主级数表示
离散级数表示
矩阵系数
准平方可积
平方可积
实矩阵乘法群
Principal series representation
Dicrete series re presentation
Matrix coefficie nt
Pre-square integrable
Square integrable.
