Galois representations attached to representations of GU(3)

For a fixed prime we compute the -adic Lie algebra of the image of the -adic Galois representation attached to a stable cuspidal automorphic representation of the unitary similitude group GU(3). This result depends on whether 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 such that is the Galois representation attached to the unitary adjoint lift of a cuspidal representation of GL(2). Received: 22 November 1999 / Accepted: 25 July 2000 / Published online: 23 July 2001