Geodesic
Certain extensions of completely splittable modules
Izvestiya. Mathematics , Tome 68 (2004) no. 4, pp. 833-850

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We obtain a formula for $\operatorname{Ext}^1_{K\Sigma_r}(D^\lambda,D^\mu)$ where $K$ is a field of characteristic grater than 2, $\Sigma_r$ is the symmetric group of degree $r$, $D^\lambda$ and $D^\mu$ are simple $K\Sigma_r$-modules, $D^\lambda$ is a completely splittable module, and $\lambda$ does not strictly dominate $\mu$. 
@article{IM2_2004_68_4_a5,
     author = {V. V. Shchigolev},
     title = {Certain extensions of completely splittable modules},
     journal = {Izvestiya. Mathematics },
     pages = {833--850},
     publisher = {mathdoc},
     volume = {68},
     number = {4},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_4_a5/}
}
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V. V. Shchigolev. Certain extensions of completely splittable modules. Izvestiya. Mathematics , Tome 68 (2004) no. 4, pp. 833-850. http://geodesic.mathdoc.fr/item/IM2_2004_68_4_a5/