Was lange währt, wird endlich gut. Abstract We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for… (More)
This is a second paper on quotients of Hom-functors and their applications to the representation theory of nite general linear groups in non-describing characteristic. After some general result on quotients of Hom-functors and their connection to Harish-Chandra theory these contructions are used to obtain a full classiication of thè-modular irreducible… (More)
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)
In this paper we use the Hecke algebra of type B to define a new algebra S which is an analogue of the q–Schur algebra. We construct Weyl modules for S and obtain, as factor modules, a family of irre-ducible S–modules over any field.
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)
This paper studies a q-deformation, B n r,s (q), of the walled Brauer algebra (a certain subalgebra of the Brauer algebra) and shows that the centralizer algebra for the action of the quantum group U R (gl n) on mixed tensor space (R n) ⊗r ⊗ (R n) * ⊗s is generated by the action of B n r,s (q) for any commutative ring R with one and an invertible element q.
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)