Triality and adjoint lifting for GL(3)

TL;DR

This paper employs the stable twisted trace formula for triality to establish the adjoint lifting of cuspidal GL(3) representations to GL(8), with implications for Ramanujan bounds and the Artin conjecture.

Contribution

It introduces a novel approach using the stable twisted trace formula for triality to lift cuspidal representations from GL(3) to GL(8).

Findings

Established the adjoint lifting of cuspidal GL(3) representations to GL(8).

Described possible isobaric decompositions of automorphic representations on GL(8).

Discussed applications to Ramanujan bounds and the strong Artin conjecture.

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.