On double centralizer properties between quantum groups and Ariki-Koike algebras.
The authors study the double centralizer properties for tensor spaces as bimodules over quantum groups and Ariki-Koike algebras [\textit{S. Ariki} and \textit{K. Koike}, Adv. Math. 106, No. 2, 216-243 (1994; Zbl 0840.20007)] and their relations with \textit{T. Shoji}'s algebras \(H^h\) [J. Algebra 226, No. 2, 818-856 (2000; Zbl 0959.20007)]. It is proved that, under the separation condition, [\textit{S. Ariki}, J. Reine Angew. Math. 513, 53-69 (1999; Zbl 0972.17011)], the natural homomorphism from the Ariki-Koike algebra to the endomorphism algebra of tensor space as module over quantum group is surjective. It is also proved that the natural homomorphism from Shoji's algebra \(H^h\) to the endomorphism algebra is always surjective, and \(H^h\) is actually isomorphic to a direct sum of matrix algebras over some Hecke algebras of type \(A\).
scientific article; zbMATH DE number 2105801
scientific article