### 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 language | English |
---|---|

Pages (from-to) | 570-587 |

Number of pages | 18 |

Journal | Journal of Algebra |

Volume | 450 |

DOIs | |

Publication status | Published - 15 Mar 2016 |

Externally published | Yes |

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

## Cite this

GLASBY, S., Praeger, C., & Xia, B. (2016). Decomposing modular tensor products, and periodicity of 'Jordan partitions'.

*Journal of Algebra*,*450*, 570-587. https://doi.org/10.1016/j.jalgebra.2015.11.025