Multiplicity free and completely reducible tensor products for SL₃(\Bbbk) and Sp₄(\Bbbk)

2024/09/12 by Gruber, Jonathan, Mancini, Gaëtan
#20G05 (primary) #51F15 (secondary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2409.07888

Abstract

Let G be a simple algebraic group over an algebraically closed field \Bbbk of positive characteristic. We consider the questions of when the tensor product of two simple G-modules is multiplicity free or completely reducible. We develop tools for answering these questions in general, and we use them to provide complete answers for the groups G = SL₃(\Bbbk) and G = Sp₄(\Bbbk).

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