Addendum: Specht modules for column-convex diagrams: Characteristic-free results for Weyl modules
Specht modules are used in the construction of the irreducible representations of \(S_n\), the symmetric group on \(n\) letters. Every \(n\)-element subset of the plane \(\mathbb{Z}\times\mathbb{Z}\) is called a diagram and to every diagram \(D\) there corresponds a Specht module \(S^D\). In the previous paper with \textit{V. Reiner} [J. Algebra 174, No. 2, 489-522 (1995; Zbl 0835.20021)], the author gave a composition series for \(S^D\), over fields of characteristic zero, in the cases that \(D\) is column-convex or when \(D\) is the complement of a column-convex diagram. It follows from the Schur-Weyl duality that the analogous results hold for the Weyl module \(K_D\) over a field of characteristic zero. In the paper under review the author shows that these results hold over any commutative ring.
scientific article; zbMATH DE number 1038268