Blocks of cyclotomic Hecke algebras

Details Blocks of cyclotomic Hecke algebras Blocks of cyclotomic Hecke algebras

2006-07-19

arxiv.org/abs/math/0607451v4

Adv. Math, Volume 216, Issue 2, 20 December 2007, Pages 854-878

Mathematics

Representation Theory

Final version. To appear in Advances in Mathematics

Scientific paper

10.1016/j.aim.2007.06.008

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.

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