Theta lifting for some cohomologicaly induced representations

Mathieu Cossutta (1, 2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 EPFL - Ecole Polytechnique Fédérale de Lausanne

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.

Mots clés: theta correspondance

Domaines: Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Mathieu Cossutta. Theta lifting for some cohomologicaly induced representations. 2009. ⟨hal-00418299⟩