Decomposition of Tensor Products of Modular Irreducible Representations for SL₃: the p ≥ 5 case

2011/11/24 by C. Bowman, Bowman, C., Stephen Doty +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #FOS: Mathematics #Representation Theory (math.RT) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1111.5811

openalex publication_date 2011/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the structure of the indecomposable direct summands of tensor products of two restricted simple SL₃(K)-modules, where K is an algebraically closed field of characteristic p ≥ 5. We give a characteristic-free algorithm for the computation of the decomposition of such a tensor product into indecomposable modules. The p<5 case for \SL₃(K) was studied in the authors' earlier paper. In this paper we show that for characteristics p≥ 5 all the indecomposable summands are rigid, in contrast to the situation in characteristic 3.

Related

• Decomposition of tensor products of modular irreducible representations for SL₃ (With an Appendix by C.M. Ringel)
• Decompositions of the tensor products of irreducible sl(2)-modules in characteristic 3
• Decomposition of tensor products of modular irreducibles for \SL₂
• Multiplicity-free tensor products of irreducible modules over simple algebraic groups in positive characteristic
• Tensor Powers of Indecomposable Modules for F\mathfrakS_p