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.

Key Words:

• Jordan partition

2010 Mathematics Subject Classification:

• 20C20

ACKNOWLEDGMENT

This work was done when the author was on sabbatical and he thanks Allegheny College for its support.

Notes

Communicated by A. Turull.