Abstract
The cyclotomic Hecke algebras Hn,r = Hn(u1, . . . , ur; q) were defined by Ariki and Koike in [AK] as Iwahori-Hecke algebras of the complex reflection group Gn,r = Sn o (Z/rZ) where Sn is the symmetric group. If ζ is a primitive complex rth root of unity, then when q → 1 and ui → ζ, the algebra Hn,r specializes to the group algebra C[Gn,r]. The irreducible representations of Hn,r are constructed in [AK]. They are indexed by the set of all r-tuples of partitions with a total of n boxes, called r-partitions. For each r-partition μ, T. Shoji [Sho] defines a symmetric function qμ and proves that qμ = ∑
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