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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.

Decomposition Matrices for the Generic Hecke Algebras on 3 Strands in Characteristic 0