Title
Theta correspondence I - Semistable range: Construction and irreducibility
Document Type
Article
Publication Date
5-1-2000
Abstract
The main purpose of this paper is to study theta correspondence from representation theoretic point of view. There are two problems we have in mind. One is the construction of unipotent representations of semisimple Lie group. The other is the parametrization of unitary dual of semisimple Lie group. In the first paper of this series, we define semistable range in the domain of theta correspondence. Roughly speaking, semistable range is a range where one can define certain averaging operator analytically. In this paper, we prove that if the averaging operator is not vanishing, then it produces the theta correspondence. This paper pave the way to study theta correspondence using analytic machinery. © World Scientific Publishing Company.
Publication Source (Journal or Book title)
Communications in Contemporary Mathematics
First Page
255
Last Page
283
Recommended Citation
He, H. (2000). Theta correspondence I - Semistable range: Construction and irreducibility. Communications in Contemporary Mathematics, 2 (2), 255-283. Retrieved from https://repository.lsu.edu/mathematics_pubs/486