The ordinary quiver of a weight three block of the symmetric group is bipartite.
type: Item
instance of: scholarly article
title: The ordinary quiver of a weight three block of the symmetric group is bipartite.
zbMATH Open document ID: 1114.20004
author: Matthew Fayers
author: Kai Meng Tan
published in: Advances in Mathematics
publication date: 2007-02-12T00:00:00Z
review text: Let \(F\) be a field and \(A\) be a finite-dimensional \(F\)-algebra. The ordinary quiver of \(A\) is a directed multi-graph with edges indexed by isomorphism classes of simple \(A\)-modules. In the paper under review it is shown that if \(F\) is a field of characteristic \(p\geq 5\), then the ordinary quiver of any \(p\)-block \(B\) of the symmetric group \(\mathfrak S_n\) with defect \(3\) is bipartite.
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 5123968
zbMATH Keywords: symmetric groups
zbMATH Keywords: blocks
zbMATH Keywords: quivers
zbMATH Keywords: hooks
zbMATH Keywords: partitions
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: j.aim.2006.04.007
OpenAlex ID: W2036312737
cites work: Q4426036
cites work: On Certain Blocks of Schur Algebras
cites work: Filtrations in Rouquier Blocks of Symmetric Groups and Schur Algebras
cites work: Representations of wreath products of algebras
cites work: On the Representation of the Symmetric Group
cites work: Q4551559
cites work: On weight three blocks of symmetric groups in characteristic three
cites work: Irreducible Specht modules for Hecke algebras of type \(A\).
cites work: Decomposition numbers for weight three blocks of symmetric groups and Iwahori--Hecke algebras
cites work: Adjustment matrices for weight three blocks of Iwahori-Hecke algebras.
cites work: A proof of the Mullineux conjecture
cites work: On the principal blocks of finite general linear groups in non-defining characteristic
cites work: The representation theory of the symmetric groups
cites work: Q3952291
cites work: On the Ext-quiver of blocks of defect 3 of symmetric group algebras
cites work: Defect \(3\) blocks of symmetric group algebras
cites work: Defect 3 blocks of symmetric group algebras. I
cites work: \([3:2]\)-pairs of symmetric group algebras and their intermediate defect 4 blocks.
cites work: On p-quotients for spin characters
cites work: Bijections of p -Regular Partitions and p -Modular Irreducibles of the Symmetric Groups
cites work: Some decomposition numbers for Hecke algebras of general linear groups
cites work: Cartan matrices and Morita equivalence for blocks of the symmetric groups
cites work: On the principal blocks of \({\mathfrak S}_9\) and \({\mathfrak S}_{10}\) over a field of characteristic \(3\)
cites work: On the principal blocks of F[Sfr ]11 and F[Sfr ]12 over a field of characteristic 3
cites work: Equivalent blocks of finite general linear groups in non-describing characteristic.
DOI: 10.1016/J.AIM.2006.04.007
description: scientific article; zbMATH DE number 5123968