The weight in a Serre-type conjecture for tame n-dimensional Galois representations

TL;DR

This paper proposes a new Serre-type conjecture for n-dimensional Galois representations that are tamely ramified at p, predicting weights via a representation-theoretic approach, with computational and theoretical evidence for specific cases.

Contribution

It introduces a novel conjecture for tamely ramified n-dimensional Galois representations and provides computational and theoretical support for certain cases.

Findings

New weights predicted for n=3 not covered by previous conjectures

Computational evidence supports the predicted weights for n=3

Theoretical evidence for n=4 using automorphic inductions

Abstract

We formulate a Serre-type conjecture for n-dimensional Galois representations that are tamely ramified at p. The weights are predicted using a representation-theoretic recipe. For n = 3 some of these weights were not predicted by the previous conjecture of Ash, Doud, Pollack, and Sinnott. Computational evidence for these extra weights is provided by calculations of Doud and Pollack. We obtain theoretical evidence for n = 4 using automorphic inductions of Hecke characters.