A Frobenius formula for the characters of Ariki-Koike algebras
type: Item
instance of: scholarly article
title: A Frobenius formula for the characters of Ariki-Koike algebras
zbMATH Open document ID: 0959.20007
author: Toshiaki Shoji
published in: Journal of Algebra
publication date: 2001-01-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 1448613
zbMATH Keywords: Ariki-Koike algebras
zbMATH Keywords: presentations
zbMATH Keywords: Schur-Weyl reciprocity
zbMATH Keywords: irreducible representations
zbMATH Keywords: primitive idempotents
zbMATH Keywords: Frobenius formula
zbMATH Keywords: characters
zbMATH Keywords: symmetric functions
reviewed by: R. M. Green
MaRDI profile type: Publication
full work available at URL: jabr.1999.8178
OpenAlex ID: W2055206750
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DOI: 10.1006/JABR.1999.8178
description: scientific article; zbMATH DE number 1448613