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Decomposition matrices for the generic Hecke algebras on 3 strands in characteristic 0. (English) Zbl 1454.20008
Summary: We determine all the decomposition matrices of the generic Hecke algebras on 3 strands in characteristic 0. These are the generic Hecke algebras associated with the exceptional complex reflection groups \(G_4, G_8\), and \(G_{16}\). We prove that for every choice of the parameters that define these algebras, all simple representations of the specialized algebra are obtained as modular reductions of simple representations of the generic algebra.
20C08 Hecke algebras and their representations
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20F36 Braid groups; Artin groups
Full Text: DOI
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