On some extensions of $p$-restricted completely splittable $\mathrm{GL}(n)$-modules
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 2, pp. 219-226.

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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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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/

[1] Schigolev V. V., “O nekotorykh rasshireniyakh vpolne rasscheplyaemykh modulei”, Izv. RAN. Ser. mat., 68:4 (2004), 131–150

[2] Brundan J., Kleshchev A. S., “Modular Littlewood–Richardson coefficients”, Math. Z., 232 (1999), 287–320 | DOI | MR | Zbl

[3] Brundan J., Kleshchev A. S., Suprunenko I. D., “Semisimple restrictions from $\mathrm{GL}(n)$ to $\mathrm{GL}(n-1)$”, J. Reine Angew. Math., 500 (1998), 83–112 | MR | Zbl

[4] Green J. A., Polynomial Representations of $\mathrm{GL}_n(K)$, Lecture Notes in Mathematics, 830, Springer, Berlin, 1980 | MR | Zbl

[5] James G. D., The Representation Theory of the Symmetric Groups, Lecture Notes in Mathematics, 682, Springer, Berlin, 1978 | MR | Zbl

[6] Jantzen J. C., Representations of Algebraic Groups, Pure and Applied Mathematics, 131, Academic Press, Boston, 1987 | MR | Zbl

[7] Kleshchev A. S., “Completely splittable representations of symmetric groups”, J. Algebra, 181:2 (1996), 584–592 | DOI | MR | Zbl