Decomposing modular tensor products: ‘Jordan partitions’, their parts and p-parts

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    Abstract

    © 2015, Hebrew University of Jerusalem. Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this decomposition in the literature, it is difficult to predict the output of these algorithms. We call a decomposition of the form (Formula presented.) a ‘Jordan partition’. We prove several deep results concerning the p-parts of the λi where p is the characteristic of the underlying field. Our main results include the proof of two conjectures made by McFall in 1980, and the proof that lcm(r, s) and gcd(λ1, …, λb) have equal p-parts. Finally, we establish some explicit formulas for Jordan partitions when p = 2.
    Original languageEnglish
    Pages (from-to)215-233
    JournalIsrael Journal of Mathematics
    Volume209
    Issue number1
    DOIs
    Publication statusPublished - Sep 2015

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