On the action of Ariki-Koike algebras on tensor space.
The author introduces a new algebra \(\mathcal H\) by generators and relations which always satisfies the double centralizer property with a Levi subalgebra of some \(q\)-Schur algebra. With these new algebras, she shows that the Ariki-Koike algebra is isomorphic to a direct sum of matrix rings over some smaller Ariki-Koike algebra when the separation condition holds, which gives a refinement of the Dipper-Mathas Morita equivalence. She also compares this new algebra \(\mathcal H\) with Shoji's modified Ariki-Koike algebra and proves that they are isomorphic to each other when \(u_i-u_j\) is invertible for any \(i\neq j\).
scientific article; zbMATH DE number 5300813
scientific article