Standard Jordan partitions with three parameters
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2017-11-20
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Barry, Michael J. J.
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20C20 , Standard Jordan partition
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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.
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Mathematics
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Barry, M.J.J. (2017). Standard Jordan partitions with three parameters. Archiv der Mathematik 109. doi:10.1007/s00013-017-1125-1
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Published article
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Springer