Automorphic Forms, Cohomology and CAP Representations. The Case $G{L}_2$ over a definite quaternion algebra

Abstract

In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=G{L}_2$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree 1. The latter ones turn out to be CAP-representations, though $G$ satisfies Strong Multiplicity One. A non-vanishing result on intertwining operators of induced representations will serve as a starting point for further investigations concerning rationality of critical $L$-values.

In (.v4) two different versions of this paper were compiled in one single file by mistake. In order to correct that I uploaded this new version

References in corpus (1)

• Cuspidal representations of reductive groups

Cited by in corpus (2)

• On some arithmetic properties of automorphic forms of GL(m) over a division algebra
• Lifting to GL(2) over a quaternion division algebra and an explicit construction of CAP representations