On a Question of Glasby, Praeger, and Xia

Abstract

A Jordan partition λ(m, n, p) = (λ1, λ2, … , λ m ) is a partition of mn associated with the expression of a tensor V m ⊗ V n of indecomposable KG-modules into a sum of indecomposables, where K is a field of characteristic p and G a cyclic group of p-power order. It is standard if λ i = m + n − 2i + 1 for all i. We answer a recent question of Glasby, Praeger, and Xia who asked for necessary and sufficient conditions for λ(m, n, p) to be standard.