A New Algorithm for Decomposing Modular Tensor Products
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Issue Date
2021-01-11
Authors
Barry, Michael J.
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This version of the article is available for viewing to the public after July 11, 2021.
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Keywords
Indecomposable representation , Tensor products
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Abstract
Let p be a prime and let Jr denote a full r×r Jordan block matrix with eigenvalue 1 over a field F of characteristic p. For positive integers r and s with r≤s , the Jordan canonical form of the rs×rs matrix Jr⊗Js has the form Jλ1⊕Jλ2⊕⋯⊕Jλr . This decomposition determines a partition λ(r,s,p)=(λ1,λ2,…,λr) of rs . Let n1,…,nk be the multiplicities of the distinct parts of the partition and set c(r,s,p)=(n1,…,nk) . Then c(r,s,p) is a composition of r. We present a new bottom-up algorithm for computing c(r,s,p) and λ(r,s,p) directly from the base-p expansions for r and s.
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Department
Mathematics
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Accepted for Publication. CC BY-NC-ND
© 2020 Australian Mathematical Publishing Association Inc.
Citation
BARRY, M. (2021). A NEW ALGORITHM FOR DECOMPOSING MODULAR TENSOR PRODUCTS. Bulletin of the Australian Mathematical Society, 104(1), 94-107. doi:10.1017/S0004972720001379
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Cambridge University Press