A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
type: Item
instance of: scholarly article
title: A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
zbMATH Open document ID: 0840.20007
author: Susumu Ariki
author: Kazuhiko Koike
published in: Advances in Mathematics
publication date: 1996-06-30T00:00:00Z
review text: Let \(G_{n,r}=(\mathbb{Z}/r\mathbb{Z})\wr S_n\) be the wreath product of \(\mathbb{Z}/r\mathbb{Z}\) with \(S_n\). In this paper, the structure of the generic Hecke algebra \(H_{n,r}\) of \(G_{n,r}\) over the algebra \(A_0=\mathbb{Z}[q,q^{-1},u_1,\dots,u_r]\) is studied and the irreducible representations of \(G_{n,r}\) over the quotient field \(K_0\) of \(A_0\) are classified. When we specify \(r\) and \(u_1\) in \(H_{n,r}\) one gets the generic Hecke algebra of type \(A_n\) and \(B_n\). So the results of this paper can be applied to the Hecke algebras \(A_n\) and \(B_n\) as special cases. In particular the centre of \(H_{n,r}\) is given explicitly.
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 638527
zbMATH Keywords: wreath products
zbMATH Keywords: generic Hecke algebras
zbMATH Keywords: irreducible representations
zbMATH Keywords: centre
reviewed by: Ahmed A. Khammash
MaRDI profile type: Publication
full work available at URL: aima.1994.1057
OpenAlex ID: W1996321859
DOI: 10.1006/AIMA.1994.1057
description: scientific article; zbMATH DE number 638527