Galois representations attached to representations of GU(3)

Abstract

For a fixed prime ∈ Z we compute the -adic Lie algebra of the image of theadic Galois representation ρ attached to a stable cuspidal automorphic representation π of the unitary similitude group GU (3). This result depends on whether π admits extra twists in the sense defined below. Two cases emerge: orthogonal image and non-orthogonal image. We show that in the orthogonal case there exists a character ν such that ρ ⊗ ν is the Galois representation attached to the unitary adjoint lift of a cuspidal representation of GL(2).