Blocks of cyclotomic Hecke algebras

Abstract

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.

Final version. To appear in Advances in Mathematics

References in corpus (1)

• Centers of degenerate cyclotomic Hecke algebras and parabolic category O

Cited by in corpus (7)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Centers of degenerate cyclotomic Hecke algebras and parabolic category O
• Core blocks of Ariki-Koike algebras II: the weight of a core block
• Rouquier blocks of the cyclotomic Ariki-Koike algebras
• Hecke-Clifford superalgebras and crystals of type $D_l^{(2)}$
• Representation Theory of Symmetric Groups and Related Hecke Algebras