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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)

The cyclotomic q-Schur algebra was introduced by Dipper, James and Mathas, in order to provide a new tool for studying the Ariki-Koike algebra. We here prove an analogue of Jantzen's sum formula for the cyclotomic q-Schur algebra. Among the applications is a criterion for certain Specht modules of the Ariki-Koike algebras to be irreducible.

- Richard Dipper
- 1998

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)

- RICHARD DIPPER, STEPHEN DOTY, JUN HU
- 2007

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.

- Richard Dipper
- 1996

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)