Decomposing modular tensor products, and periodicity of 'Jordan partitions'

Stephen GLASBY, Cheryl Praeger, Binzhou Xia

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let Jr denote an r×r matrix with minimal and characteristic polynomials (t-1)r. Suppose r=s. It is not hard to show that the Jordan canonical form of Jr¿Js is similar to J¿1¿¿¿J¿r where ¿1=¿=¿r>0 and ¿i=1r¿i=rs. The partition ¿(r, s, p):=(¿1, . . ., ¿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 ¿(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 ¿(r, s, p) for all s and p, with s=r and p prime.
Original languageEnglish
Pages (from-to)570-587
Number of pages18
JournalJournal of Algebra
Volume450
DOIs
Publication statusPublished - 15 Mar 2016
Externally publishedYes

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