Geodesic
Representations of algebraic groups of type $D_n$ in characteristic 2 with small weight multiplicities
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 18, Tome 365 (2009), pp. 182-195 
A. A. Osinovskaya; I. D. Suprunenko. Representations of algebraic groups of type $D_n$ in characteristic 2 with small weight multiplicities. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 18, Tome 365 (2009), pp. 182-195. http://geodesic.mathdoc.fr/item/ZNSL_2009_365_a9/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Lower estimates for the maximal weight multiplicities in irreducible representations of the algebraic groups of type $D_n$ in characteristic 2 are found. If $n\geq8$, then either such multiplicity is at least $n-4-[n]_4$, where $[n]_4$ is the residue of $n$ modulo 4, or all weight multiplicities are equal to 1. For groups of types $B_n$ and $D_n$ in odd characteristic and of type $C_n$ in characteristic $>7$ similar results were obtained earlier. Bibl. – 11 titles.

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[2] N. Burbaki, Gruppy i algebry Li, Gl. IV–VI, Mir, M., 1972 | MR | Zbl

[3] N. Burbaki, Gruppy i algebry Li, Gl. VII–VIII, Mir, M., 1978 | MR

[4] A. E. Zalesskii, I. D. Suprunenko, “Predstavleniya razmernostei $(p^n\pm1)$ simplekticheskoi gruppy stepeni $2n$ nad konechnym polem”, Vesti AN BSSR. Cer. fiz.-mat. nauk, 1987, no. 6, 9–15 | MR

[5] A. A. Baranov, I. D. Suprunenko, “Branching rules for modular fundamental representations of symplectic groups”, Bull. London Math. Soc., 32 (2000), 409–420 | DOI | MR | Zbl

[6] A. Borel, “Properties and linear representations of Chevalley groups”, Seminar on Algebraic Groups and Related Finite Groups, Lect. Notes Math., 131, eds. A. Borel et al., 1970, 1–55 | DOI | MR

[7] J. C. Jantzen, Darstellungen halbeinfacher algebraischer Gruppen und zugeordnete kontravariante Formen, Bonner Math. Schr., 67, 1973 | MR | Zbl

[8] G. M. Seitz, “The maximal subgroups of classical algebraic groups”, Memoirs of the AMS, 365 (1987), 1–286 | MR

[9] S. Smith, “Irreducible modules and parabolic subgroups”, J. Algebra, 75 (1982), 286–289 | DOI | MR | Zbl

[10] R. Steinberg, “Representations of algebraic groups”, Nagoya Math. J., 22 (1963), 33–56 | MR | Zbl

[11] I. D. Suprunenko, “On Jordan blocks of elements of order $p$ in irreducible representations of classical groups with $p$-large highest weights”, J. Algebra, 273 (1997), 589–627 | DOI | MR