Theta lifting for some cohomologicaly induced representations

TL;DR

This paper generalizes the automorphicity of certain cohomological representations of U(a,b) via theta lifting, extending previous results and proving new cases of Adams conjecture.

Contribution

It extends Li's results to a broader class of cohomological representations of U(a,b) using theta correspondence and cohomological induction.

Findings

Generalization of automorphicity for more cohomological representations

Proof of some cases of Adams conjecture

Connection between cohomological induction and theta correspondence

Abstract

In his paper 'Theta lifting for representations with non zero cohomlogy', Jian-Shu Li proved that a certain kind of cohomological representations of $U(a,b)$ is automorphic. In this paper, this result is generalized to a more general class of cohomological representations of this group. It comes from the fact that these cohomological representations are the image by the theta correspondance of some representations obtained by cohomological induction. In proving this theorem, we also prove some cases of Adams conjecture.