A Frobenius formula for the characters of Ariki-Koike algebras
The author considers the Ariki-Koike algebra \({\mathcal H}_{n,r}\) and gives a new presentation of it which arises naturally in the context of the analogue of the Schur-Weyl reciprocity established by Sakamoto and Shoji. The complete set of irreducible representations of \({\mathcal H}_{n,r}\) is then obtained by inducing modules from a family of subalgebras which are given in terms of the new presentation. Orthogonal primitive idempotents are then constructed. Finally, the author develops a Frobenius formula for the characters by adapting the theory of symmetric functions to multipartitions, thus generalizing work of \textit{A. Ram} [Invent. Math. 106, No. 3, 461-488 (1991; Zbl 0758.05099)] in the type \(A\) case.
scientific article; zbMATH DE number 1448613