Companion forms for unitary and symplectic groups

TL;DR

This paper proves a companion forms theorem for automorphic Galois representations, establishing new results on Serre weights and automorphic representations for unitary and symplectic groups using automorphy lifting and functoriality.

Contribution

It introduces a novel method combining automorphy lifting and functoriality to establish companion forms theorems for unitary and symplectic groups.

Findings

Proves a companion forms theorem for automorphic Galois representations.

Deduces Serre weight possibilities for mod l Galois representations.

Extends results to automorphic representations of GSp4 over totally real fields.

Abstract

We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first author. We deduce results about the possible Serre weights of mod l Galois representations corresponding to automorphic representations on unitary groups. We then use functoriality to prove similar results for automorphic representations of GSp4 over totally real fields.