This article is cited in 1 paper

On extensions and branching rules for modules close to completely splittable

V. V. Shchigolev

Ulyanovsk State University

Abstract: 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.

UDC: 512.547.2

MSC: 20C30

Received: 13.09.2004

DOI: 10.4213/sm1408

 English version: Sbornik: Mathematics, 2005, 196:8, 1209–1249

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