Blocks of affine and cyclotomic Hecke algebras

Sinead Lyle and Andrew Mathas


This paper classifies the blocks of the affine Hecke algebras of type A and the blocks of the cyclotomic Hecke algebras of type G(r,1,n) over an arbitrary algebraically closed 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'. <p> 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.

Keywords: Affine Hecke algebras, Cyclotomic Hecke algebras, cyclotomic Schur algebras, blocks.

AMS Subject Classification: Primary 20C08; secondary 20C30, 05E10.

This paper is available as a pdf (248kB) file.
Wednesday, August 2, 2006