Decomposition of tensor products of modular irreducible representations for SL3: The p ≥ 5 case

Chris Bowman-Scargill, Stephen Doty, S Martin

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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.
Original languageEnglish
Pages (from-to)105-138
Number of pages34
JournalInternational Electronic Journal of Algebra
Volume2017
Publication statusPublished - 1 Jan 2015

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