Weights of multipartitions and representations of Ariki-Koike algebras. II: Canonical bases (Q926850): Difference between revisions

The author continues his study of Ariki-Koike algebras (cyclotomic Hecke algebras) begun in [Adv. Math. 206, No. 1, 112--144 (2006; Zbl 1111.20009)] where he introduced a notion of `weight' for multipartitions. Here he considers the canonical basis for an integrable highest-weight module of the quantum algebra \(U_v(\widehat{\mathfrak{sl}}_e)\) and shows how the relationship between different canonical bases is controlled by the weight of a multipartition, generalizing a theorem of \textit{A. Lascoux, B. Leclerc} and \textit{J.-Y. Thibon} [Commun. Math. Phys. 181, 205--263 (1996; Zbl 0874.17009)] for the level 1 case.