Analysis reveals conditions for tensor products being multiplicity free in SL3 and Sp4, suggesting broader implications in algebraic group theory.
Let G be a simple algebraic group over an algebraically closed field 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 = SLโ( ) and G = Spโ( ) .
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Gruber et al. (2026) studied this question.
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