On endomorphism algebras arising from Hecke algebras
type: Item
instance of: scholarly article
title: On endomorphism algebras arising from Hecke algebras
zbMATH Open document ID: 0923.16026
author: Hebing Rui
published in: Journal of Algebra
publication date: 1999-09-07T00:00:00Z
review text: The endomorphism algebras associated to Hecke algebras of type \(D\) with odd ranks are studied. A number of authors have studied the cases when the endomorphism algebras are associated to the Hecke algebras of types \(A_{n-1}\), \(B_n\) and \(C_n\) or more generally, \(G(r,1,n)\). It turns out that the cellular basis (or more generally, standard basis) of Hecke algebras is important in the study of these endomorphism algebras. The notion of standardly based algebras was introduced by \textit{J. Du} and \textit{H. Rui} [in Trans. Am. Math. Soc. 350, No. 8, 3207-3235 (1998; Zbl 0908.16015)] and these are generalized versions of cellular algebras introduced by \textit{J. J. Graham} and \textit{G. I. Lehrer} [in Invent. Math. 123, No. 1, 1-34 (1996; Zbl 0853.20029)]. Two standard bases for Hecke algebras \(\mathcal H\) of type \(D\) with odd ranks are constructed in this paper under the assumption that a certain polynomial in \(q\) is nonzero. It is then shown that the endomorphism algebras associated to Hecke algebras \(\mathcal H\) are standardly based algebras and indeed quasi-hereditary.
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1275268
zbMATH Keywords: endomorphism algebras
zbMATH Keywords: Hecke algebras
zbMATH Keywords: cellular bases
zbMATH Keywords: standardly based algebras
zbMATH Keywords: cellular algebras
zbMATH Keywords: standard bases
MaRDI profile type: Publication
full work available at URL: jabr.1998.7684
OpenAlex ID: W2020206565
cites work: A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
cites work: Q3804882
cites work: Representations of Hecke Algebras of General Linear Groups
cites work: The (Q, q )-Schur Algebra
cites work: Cyclotomic \(q\)-Schur algebras
cites work: Hecke Algebras of Type Bn at Roots of Unity
cites work: Based algebras and standard bases for quasi-hereditary algebras
cites work: The 𝑞-Schur² algebra
cites work: Cellular algebras
cites work: The representations of Hecke algebras of type \(A_ n\)
cites work: Representations of Hecke algebras of type \(D_ n\)
cites work: On endomorphism algebras arising from multiparameter Hecke algebras
cites work: The partial order on two-sided cells of certain affine Weyl groups
DOI: 10.1006/JABR.1998.7684
description: scientific article; zbMATH DE number 1275268