On the characters of unitary representations

Journal of the Australian Mathematical Society

Michael Cowling¹ 

关键词: 22 D 10;    22 D 25;   

DOI  :  10.1017/S1446788700032262

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let G be a locally compact group, and let D(G) be a dense subalgebra of the convolution algebra L1(G). Suppose that π is a unitary representation of G and that, for each u in D(G), π(u)) is a trace-class operator. Then the linear functional u → tr(π(u)) (the trace of π(u)) is called the D-character of π. We give a simple proof that the D-character of such a representation determines the representation up to unitary equivalence. As an application, we give an easy proof of the result of Harish-Chandra that the K-finite characters of unitary representations of semisimple Lie groups determine the representations.

【 授权许可】

Unknown