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Standard Jordan partitions with three parameters

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Author(s)
Barry, Michael J. J.
Date Issued
November 20, 2017
Abstract
We extend previous work on standard two-parameter Jordan partitions by Barry (Commun Algebra 43:4231–4246, 2015) to three parameters. Let Jr denote an r×r matrix with minimal polynomial (t−1)r over a field F of characteristic p. For positive integers n1, n2, and n3 satisfying n1 ≤ n2 ≤ n3, the Jordan canonical form of the n1n2n3 × n1n2n3 matrix Jn1 ⊗ Jn2 ⊗ Jn3 has the form Jλ1 ⊕ Jλ2 ⊕···⊕ Jλm where λ1 ≥ λ2 ≥ ··· ≥ λm > 0 and m i=1 λi = n1n2n3. The partition λ(n1, n2, n3 : p)=(λ1, λ2,...,λm) of n1n2n3, which depends on n1, n2, n3, and p, will be called a Jordan partition. We will define what we mean by a standard Jordan partition and give necessary and sufficient conditions for its existence.
Journal
Archiv der Mathematik
Department
Mathematics
Citation
Barry, M.J.J. (2017). Standard Jordan partitions with three parameters. Archiv der Mathematik 109. doi:10.1007/s00013-017-1125-1
Publisher
Springer
Version of Article
Published article
DOI
10.1007/s00013-017-1125-1
ISSN
0003-889X
e1420-8938
Rights
This article is published and restricted. Copyright is retained by publisher or authors. Contact the publisher for further use of this material.
Subjects

20C20

Standard Jordan parti...

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