Abstract

Given a finite group G and an abelian variety A acted on by G, to any subgroup H of G, we associate an abelian subvariety A(H) on which the associated Hecke algebra H-H for H in G acts. Any irreducible rational representation (W) over tilde of H-H induces an abelian subvariety of A(H) in a natural way. In this paper we give equations for this abelian subvariety. In a special case these equations become much easier. We work out some examples. (C) 2020 Elsevier Inc. All rights reserved.