On extensions and branching rules for modules close to completely splittable

V. V. Shchigolev

Sbornik. Mathematics, Tome 196 (2005) no. 8, pp. 1209-1249

Résumé

The modules $D^\lambda{\downarrow}_{\Sigma_{n-1}}$ and $D^\lambda{\uparrow}^{\Sigma_{n+1}}$ are described for certain simple $K\Sigma_n$-modules $D^\lambda$ (the completely splittable ones or close to them), where $K$ is a field of characteristic $p>0$ and $\Sigma_n$ is the symmetric group of degree $n$. This result is based on an upper bound for the dimensions of the $\operatorname{Ext}^1$-spaces between certain simple modules.

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