On Specht modules in the Auslander-Reiten quiver
Let \(\Lambda\) be a finite-dimensional algebra over a field \(F\). The Auslander-Reiten quiver (AR quiver) \(\Gamma(\Lambda)\) of \(\Lambda\), a certain directed graph on the isomorphism classes of indecomposable \(\Lambda\)-modules, is an important homological invariant of the algebra, and it has been of major use for studying representations. In this paper, we investigate this graph for blocks of \(F{\mathcal S}_n\) where \(F\) is an algebraically closed field of characteristic \(p\), where \(p\) is a non-zero prime dividing \(n!\) and \({\mathcal S}_n\) is the symmetric group of degree \(n\). The aim is to determine the positions of the Specht modules in \(\Gamma(B)\) where \(B\) is a block of \(F{\mathcal S}_n\) of finite or tame representation type or with elementary Abelian defect groups of order \(p^2\).
scientific article; zbMATH DE number 763946