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Branching rules for modular fundamental representations of symplectic groups. (English) Zbl 1025.20031

In the paper under review the branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group \(\text{Sp}_{2n}(K)\) to the naturally embedded subgroup \(\text{Sp}_{2n-2}(K)\) is determined. As a corollary, inductive systems of fundamental representations for \(\text{Sp}_\infty(K)\) are classified. The submodule structure of the fundamental Weyl modules is refined.

MSC:

20G05 Representation theory for linear algebraic groups
20C20 Modular representations and characters
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