Geodesic
On some extensions of $p$-restricted completely splittable $\mathrm{GL}(n)$-modules
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 2, pp. 219-226 
V. V. Shchigolev. On some extensions of $p$-restricted completely splittable $\mathrm{GL}(n)$-modules. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 2, pp. 219-226. http://geodesic.mathdoc.fr/item/FPM_2005_11_2_a14/
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     author = {V. V. Shchigolev},
     title = {On some extensions of $p$-restricted completely splittable $\mathrm{GL}(n)$-modules},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {219--226},
     year = {2005},
     volume = {11},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_2_a14/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we calculate the space $\mathrm{Ext}_{\mathrm{GL}(n)}(L_n(\lambda),L_n(\mu))$, where $\mathrm{GL}(n)$ is the general linear group of degree $n$ over an algebraically closed field of positive characteristic, $L_n(\lambda)$ and $L_n(\mu)$ are rational irreducible $\mathrm{GL}(n)$-modules with highest weights $\lambda$ and $\mu$, respectively, the restriction of $L_n(\lambda)$ to any Levi subgroup of $\mathrm{GL}(n)$ is semisimple, $\lambda$ is a $p$-restricted weight, and $\mu$ does not strictly dominate $\lambda$.

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