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Endomorphism algebras of 2-row permutation modules in characteristic 3. (English) Zbl 1480.20025

Summary: Given \(r \in \mathbb{N}\), let \(\lambda\) be a partition of \(r\) with at most two parts. Let F be a field of characteristic 3. Write \(M^\lambda\) for the \(\mathbf{F} S_r\)-permutation module corresponding to the action of the symmetric group \(S_r\) on the cosets of the maximal Young subgroup \(S_\lambda\). We construct a full set of central primitive idempotents in \(\mathrm{End}_{\mathbf{F} S_r}(M^\lambda)\) in this case. We also determine the Young module corresponding to each primitive idempotent that we construct.

MSC:

20C20 Modular representations and characters
20C30 Representations of finite symmetric groups
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References:

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