It is well-known that there is a strong link between the representation
theories of the general linear group and the symmetric group over the
complex numbers. J.A.Green has shown that this in also true over infinite
fields of positive characteristic. For this he used the Schur functor as
introduced by I.Schur in his PhD thesis.
In this talk I will show that one can do the same thing for the symplectic
group and the Brauer algebra. This is joint work with S.Donkin. As a
consequence we obtain that (under certain conditions) the Brauer algebra and
the symplectic Schur algebra in characteristic p have the same block
relation. Furthermore we obtain a new proof of the description of the blocks
of the Brauer algebra in characteristic zero as obtained by Cox, De Visscher
and Martin.