Brauer Algebras, Symplectic Schur Algebras and Schur-weyl Duality
نویسندگان
چکیده
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 Bn(−2m) to the endomorphism algebra of the tensor space (K2m)⊗n as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is always surjective. Another surjectivity, that of the natural homomorphism from the group algebra for GSp2m(K) to the endomorphism algebra of (K2m)⊗n as a module over Bn(−2m), is derived as an easy consequence of S. Oehms’s results [S. Oehms, J. Algebra (1) 244 (2001), 19–44].
منابع مشابه
Schur Algebras and Schur - Weyl Duality
In this paper we study Schur-Weyl duality between the symplectic group and Brauer’s centralizer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer’s centralizer algebra Bn(−2m) to the endomorphism algebra of tensor space (K) as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is...
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