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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 ppower exceeding r. This generalizes results of J.A. Green, B. Srinivasan, and others which depend on the smallest ppower 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 

Pages (fromto)  570587 
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
 1 Finished

Symmetry & Computation
Praeger, C., Niemeyer, A. & Seress, A.
ARC Australian Research Council
1/01/11 → 31/12/15
Project: Research