On the Semi-simplicity of the Hecke Algebra of (Z/rZ) ≀ Sn

Crystal bases and simple modules for Hecke algebras of type $G(p,p,n)$

“…Let vΛ (resp., v Λ ) denote the unique highest weight vector of highest weightΛ (resp., of highest weight Λ) inB(Λ) (resp., in B(Λ)). Therefore, by (6.6) and Lemma 6.7, we get that = λ [i] , ∀ 1 ≤ i ≤ k. We write λ = (λ [1] , · · · , λ na k Lemma 6.16. With the above notations, the map which sends λ = λ [1] , · · · , λ [k] to λ := λ [1] , · · · , λ [a] defines a bijection from the set Σ(m) onto the set Σ(k, m).…”

“…Whenever the parameter q is clear from the context, we shall say (for simplicity) that the algebra H K (r, n) is with the parameters set {Q 1 …”

“…and we use θ to denote the map λ → (λ [1] , · · · , λ [k] ). Now we can state the first main result, which deals with the case where k = 1 and K = C. …”

“…Replacing P (1) by P, and using the definition of residue given in (2.5) for multipartition, we get a level p Fock space…”

“…H(p − s, n − b)-module), where λ [1] (resp., λ [2] ) is an s-multipartition of b (resp., (p − s)-multipartition of n − b). Let λ := (λ [1] , λ [2] ) (concatenation of ordered tuples), which is a p-multipartition of n. By [15]…”