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)⊗n as a module over the symplectic similitude group GS_p2m(K) (or equivalently, as a module over the symplectic group S_p2m(K)) is always surjective. Another surjectivity, that of the natural homomorphism from the group algebra for GS_p2m(K) to the endomorphism algebra of (K^2m)⊗n as a module over B_n(-2m), is derived as an easy consequence of S. Oehms's results [S. Oehms, J. Algebra (1) 244 (2001), 19-44].