On a Question of Glasby, Praeger, and Xia

A Jordan partition λ(m, n, p) = (λ 1 , λ 2 , ... , 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...

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Bibliographic Details
Published in:Communications in algebra 2015-10, Vol.43 (10), p.4231-4246
Main Author: Barry, Michael J. J.
Format: Article
Language:English
Subjects:
Jordan partition
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Summary:A Jordan partition λ(m, n, p) = (λ 1 , λ 2 , ... , 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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2014.941470