Triality and adjoint lifting for GL(3)

Abstract

Using the stable twisted trace formula for the triality automorphism, we show the adjoint lifting (to GL(8)) of cuspidal representations of GL(3) with a discrete series local component. We also describe the possible isobaric decompositions of the resulting automorphic representations on GL(8) and discuss applications towards Ramanujan bounds for GL(3) and the strong Artin conjecture for certain 3-dimensional Galois representations.