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We extend the family of classical Schur algebras in type A, which determine the polynomial representation theory of general linear groups over an infinite field, to a larger family, the rational Schur algebras, which determine the rational representation theory of general linear groups over an infinite field. This makes it possible to study the rational(More)
In this paper we prove the Schur-Weyl duality between the sym-plectic 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(More)
The Hecke algebra H = H R;Q;q (W n) over a commutative ring R with the two parameters Q; q associated with the Weyl group W n of type B n has certain distinguished representations aaorded by modules ~ S labelled by bipartitions of n. These are precisely the irreducible H-modules, if H is semisimple. In general there is a symmetric H-invariant bilinear form(More)
Let G be a nite group of Lie type deened over some nite eld GF(q). Let k be a eld of positive characteristic p not dividing q. Hecke functors tie together the representation theory of kG and that of Hecke algebras associated with nite reeection groups. In DDu1] the theory of vertices and sources for such algebras was introduced in the case of Hecke algebras(More)
In this paper, we show the second part of Schur-Weyl duality for mixed tensor space. The quantum group U = U(gl n) of the general linear group and a q-deformation B n r,s (q) of the walled Brauer algebra act on V ⊗r ⊗ V * ⊗s where V = R n is the natural U-module. We show that End B n r,s (q) (V ⊗r ⊗ V * ⊗s) is the image of the representation of U, which we(More)