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## Abstract

Let J(r) denote an r x r matrix with minimal and characteristic polynomials (t - 1)(r). Suppose r = ... >=lambda(r), > 0 and Sigma(r)(i=1) lambda(i) = rs. The partition lambda(r, s, p) := (lambda 1, ... , lambda(r)) of rs, which depends only on r, s and the characteristic p := char(F), has many applications including the study of algebraic groups. We prove new periodicity and duality results for lambda(r, s, p) that depend on the smallest p-power exceeding r. This generalizes results of J.A. Green, B. Srinivasan, and others which depend on the smallest p-power exceeding the (potentially large) integer s. It also implies that for fixed r we can construct a finite table allowing the computation of lambda(r, s, p) for all s and p, with s >= r and p prime. (C) 2015 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 570-587 |

Number of pages | 18 |

Journal | Journal of Algebra |

Volume | 450 |

DOIs | |

Publication status | Published - 15 Mar 2016 |

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Dive into the research topics of 'Decomposing modular tensor products, and periodicity of 'Jordan partitions''. Together they form a unique fingerprint.## Projects

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