Symplectic representations of semidirect products
I will discuss symplectic representations (over the field of complex numbers) of a group that is a semidirect product of a normal subgroup H and a cyclic group, where H is in turn a semidirect product of a normal p-group A and a finite cyclic group. Representations in question arise naturally in connection with elliptic curves over the field of rational numbers and, more generally, with abelian varieties over number fields. In this talk I will concentrate on the case when A is abelian.