TY - JOUR
T1 - Brauer algebras, symplectic schur algebras and Schur-Weyl duality
AU - Dipper, Richard
AU - Doty, Stephen
AU - Hu, Jun
PY - 2008/1
Y1 - 2008/1
N2 - 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].
AB - 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].
UR - http://www.scopus.com/inward/record.url?scp=43649108774&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-07-04179-7
DO - 10.1090/S0002-9947-07-04179-7
M3 - Article
AN - SCOPUS:43649108774
SN - 0002-9947
VL - 360
SP - 189
EP - 213
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 1
ER -