Irreducibility of Galois representations associated to low weight Siegel modular forms

If f is a cuspidal modular eigenform of weight k>1, Ribet proved that its associated p-adic Galois representation is irreducible for all primes. More generally, it is conjectured that the p-adic Galois representations associated to cuspidal automorphic representations of GL(n) should always be irreducible.

In this talk, I will prove a version of this conjecture for low weight, genus 2 Siegel modular forms. These two-dimensional analogues of weight 1 modular forms are, conjecturally, the automorphic objects that correspond to abelian surfaces.