# Decomposition of tensor products of modular irreducible representations for SL3: the p ? 5 case

Bowman, Christopher, Doty, S., Martin, S. (2015) Decomposition of tensor products of modular irreducible representations for SL3: the p ? 5 case. International Electronic Journal of Algebra, 17 (17). pp. 105-138. E-ISSN 1306-6048. (doi:10.24330/ieja.266215) (KAR id:70131)

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## Abstract

We study the structure of the indecomposable direct summands of tensor products of two restricted rational simple modules for the algebraic group SL3(K), where K is an algebraically closed field of characteristic p ? 5. We also give a characteristic-free algorithm for the decomposition of such a tensor product into indecomposable direct summands. The p < 5 case was studied in the authors’ earlier paper [4]. We find that for characteristics p ? 5 all the indecomposable summands are rigid, in contrast to the characteristic 3 case.

Item Type: Article 10.24330/ieja.266215 Algebraic groups, tilting modules, Weyl modules, quivers Q Science > QA Mathematics (inc Computing science) Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Christopher Bowman 16 Nov 2018 11:48 UTC 16 Feb 2021 13:59 UTC https://kar.kent.ac.uk/id/eprint/70131 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-6046-8930