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March 6, 2026Forum of Mathematics Sigma0 citationsOpen Access

Multiplicity free and completely reducible tensor products for SL 3 (𝕜) and Sp 4 (𝕜)

JGJonathan GruberGMGaëtan Mancini

Key Points

  • This research investigates under which conditions the tensor product of two simple G-modules is multiplicity free or completely reducible for specific algebraic groups.
  • Examined tensor products of simple modules for algebraic groups SL3 and Sp4.
  • Developed general tools for evaluating multiplicity and reducibility in G-modules.
  • Applied findings to derive specific results for SL3 and Sp4.
  • Identified clear conditions for tensor products to be multiplicity free for SL3 and Sp4.
  • Demonstrated the two groups exhibit completely reducible tensor products under specified conditions.

Abstract

Abstract 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 = SL₃ () and G = Sp₄ ().

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Cite This Study

Gruber et al. (2026) studied this question.

synapsesocial.com/papers/69aa7077531e4c4a9ff5a52bhttps://doi.org/10.1017/fms.2026.10179
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