标题： 实不可约群的主表示的性质 显示英文标题

标题： The Character of the Principal Series of Representations of the Real Unimodular Group

摘要： 主系列表示的特征通过使用Gel'fand和Naimark对特征的定义进行评估。 该表示在SL(n,R)相对于实三角矩阵子群的右陪集空间上定义的函数空间中实现。 这种表示形式大大简化了群环积分核的确定问题，这是Gel'fand-Naimark理论中特征的基本问题。 主系列表示的一个重要特点是SL(n,R)中的“椭圆”元素不对其特征做出贡献。 显示英文摘要

摘要： The character of the principal series of representations of SL(n,R) is evaluated by using Gel'fand and Naimark's definition of character. This representation is realized in the space of functions defined on the right coset space of SL(n,R) with respect to the subgroup of real triangular matrices. This form of the representations considerably simplifies the problem of determination of the integral kernel of the group ring which is fundamental in the Gel'fand-Naimark theory of character. An important feature of the principal series of representations is that the `elliptic' elements of SL(n,R) do not contribute to its character.