This paper classifies the blocks of the cyclotomic Hecke algebras of type
G(r,1,n) over an arbitrary field. Rather than working with the Hecke algebras
directly we work instead with the cyclotomic Schur algebras. The advantage of
these algebras is that the cyclotomic Jantzen sum formula gives an easy
combinatorial characterization of the blocks of the cyclotomic Schur algebras.
We obtain an explicit description of the blocks by analyzing the combinatorics
of `Jantzen equivalence'.
We remark that a proof of the classification of the blocks of the cyclotomic
Hecke algebras was announced in 1999. Unfortunately, Cox has discovered that
this previous proof is incomplete.Comment: Final version. To appear in Advances in Mathematic
This paper investigates the Rouquier blocks of the Hecke algebras of the symmetric groups and the Rouquier blocks of the q-Schur algebras. We first give an algorithm for computing the decomposition numbers of these blocks in the ``abelian defect group case'' and then use this algorithm to explicitly compute the decomposition numbers in a Rouquier block. For fields of characteristic zero, or when q=1 these results are known; significantly, our results also hold for fields of positive characteristic with q?1. We also discuss the Rouquier blocks in the ``non–abelian defect group'' case. Finally, we apply these results to show that certain Specht modules are irreducible
We prove a q-analogue of the Carter-Payne theorem for the two special cases corresponding to moving an arbitrary number of nodes between adjacent rows, or moving one node between an arbitrary number of rows. As a consequence, we show that these homomorphism spaces are one dimensional when q ? -1. We apply these results to complete the classification of the reducible Specht modules for the Hecke algebras of the symmetric groups when q ? -1. Our methods can also be used to determine certain other pairs of Specht modules between which there is a homomorphism. In particular, we describe the homomorphism space for an arbitrary partition µ
We prove analogues of (Donkin's generalisations of) James's row and column removal theorems, in the context of homomorphisms between Specht modules for symmetric groups
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