Brauer algebras, symplectic Schur algebras and Schur-Weyl duality

In this paper we prove the Schur-Weyl duality between the symplectic group and the Brauer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer algebra B(n)(-2m) to the endomorphism algebra of the tensor space (K(2m))(circle times n) as a module over the symplectic similitude group GS(p2m)(K) (or equivalently, as a module over the symplectic group Sp(2m)(K)) is always surjective. Another surjectivity, that of the natural homomorphism from the group algebra for GSp(2m)(K) to the endomorphism algebra of (K(2m))(circle times n) as a module over B(n)(-2m), is derived as an easy consequence of S. Oehms's results.