The sign of Galois representations attached to automorphic forms for unitary groups

TL;DR

This paper proves that the polarization sign of Galois representations linked to polarized automorphic forms on unitary groups over CM fields is always positive, confirming a conjecture by Gross.

Contribution

It establishes that the polarization sign for these Galois representations is always +1, providing a key confirmation of Gross's conjecture.

Findings

Polarization sign is always +1 for these Galois representations

Confirms Gross's conjecture on polarization signs

Advances understanding of automorphic Galois representations

Abstract

We determine the sign of the polarization of any polarized irreducible factor of a Galois representation attached to a polarized cohomological cuspidal automorphic form of Gl_n of a CM field: it is always +1, as was conjectured by Gross.