Knapp A W, Stein E M
Department of Mathematics, Cornell University, Ithaca, New York 14853.
Proc Natl Acad Sci U S A. 1975 Jun;72(6):2459-61. doi: 10.1073/pnas.72.6.2459.
The intertwining operators that have been constructed for all the series of unitary representations appearing in the Plancherel formula of a connected real semisimple Lie group of matrices are given a new normalization and then applied in two ways. The first is to obtain dimension formulas for the commuting algebras of the unitary representations in question. The second is to establish the existence of complementary series. These bear the same relationship to the unitary representations under study that the complementary series found earlier bear to the principal series.
为连通实半单矩阵李群的普兰切尔公式中出现的所有酉表示系列所构造的交织算子进行了新的归一化,然后以两种方式应用。第一种方式是获得相关酉表示的交换代数的维数公式。第二种方式是确立互补系列的存在性。这些互补系列与所研究的酉表示之间的关系,与早期发现的互补系列与主系列之间的关系相同。