Brauer algebras, symplectic Schur algebras and Schur-Weyl duality

By R. Dipper, Stephen R Doty, Jun Hu. 2005

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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 GSp 2m (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 )⊗ 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].

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/40994cc9ee90ac2ea30dbafbe5c093ae45e9f7d1