On the asymptotics of Harish-Chandra modules.
On the asymptotics of Harish-Chandra modules.
复制标题
关于 Harish-Chandra 模的渐进性。
DOI：
10.1515/crll.1983.343.169
复制
发表时间：
1983
期刊：
影响因子：
--
通讯作者：
Henryk Hecht
中科院分区：
文献类型：
--
作者：
W. Schmid;Henryk Hecht
在对半单李群的不可约、可接受表示的研究中，Harish-Chandra 广泛使用了矩阵系数的渐近展开式 [12]、[13]。特别是，他从渐近展开中构建了某些嵌入到主级数表示中[14]；这些想法随后被卡塞尔曼[5]扩展和完善。 Harish-Chandra 和 Casselman 都提出了渐近展开是否决定主级数表示的所有嵌入的问题。我们的主要结果是卡塞尔曼推测的一个声明，它肯定地回答了这个问题。
In his study of irreducible, admissible representations of semisimple Lie groups, Harish-Chandra makes extensive use of the asymptotic expansions of matrix coefficients [12], [13]. In particular, he constructs certain embeddings into principal series representations from the asymptotic expansions [14]; these ideas were then extended and refined by Casselman [5]. Both Harish-Chandra and Casselman raised the question whether the asymptotic expansions determine all embeddings into principal series representations. Our main result is a Statement, conjectured by Casselman, that answers the question affirmatively.