TY - JOUR

T1 - Decomposing modular tensor products, and periodicity of 'Jordan partitions'

AU - GLASBY, Stephen

AU - Praeger, Cheryl

AU - Xia, Binzhou

PY - 2016/3/15

Y1 - 2016/3/15

N2 - 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.

AB - 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.

KW - Green ring

KW - Jordan blocks

KW - Jordan canonical form

KW - Jordan partition

KW - Tensor product

UR - http://www.scopus.com/inward/record.url?scp=85000577851&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/decomposing-modular-tensor-products-periodicity-jordan-partitions

U2 - 10.1016/j.jalgebra.2015.11.025

DO - 10.1016/j.jalgebra.2015.11.025

M3 - Article

VL - 450

SP - 570

EP - 587

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -