  Turner's Conjecture describes all blocks of symmetric groups and Hecke
algebras up to derived equivalence in terms of certain double algebras. With a
view towards a proof of this conjecture, we develop a general theory of Turner
doubles. In particular, we describe doubles as explicit maximal symmetric
subalgebras of certain generalized Schur algebras and establish a Schur-Weyl
duality with wreath product algebras.
