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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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.
@article{ZNSL_2009_365_a9,
     author = {A. A. Osinovskaya and I. D. Suprunenko},
     title = {Representations of algebraic groups of type $D_n$ in characteristic~2 with small weight multiplicities},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {182--195},
     year = {2009},
     volume = {365},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_365_a9/}
}
TY  - JOUR
AU  - A. A. Osinovskaya
AU  - I. D. Suprunenko
TI  - Representations of algebraic groups of type $D_n$ in characteristic 2 with small weight multiplicities
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 182
EP  - 195
VL  - 365
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_365_a9/
LA  - ru
ID  - ZNSL_2009_365_a9
ER  - 
%0 Journal Article
%A A. A. Osinovskaya
%A I. D. Suprunenko
%T Representations of algebraic groups of type $D_n$ in characteristic 2 with small weight multiplicities
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 182-195
%V 365
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_365_a9/
%G ru
%F ZNSL_2009_365_a9
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/

[1] A. A. Baranov, A. A. Osinovskaya, I. D. Suprunenko, “Modulyarnye predstavleniya klassicheskikh grupp s malymi kratnostyami vesov”, Sovremennaya matematika i ee prilozheniya (algebra), 60, In-t Kibernetiki AN Gruzii, Tbilisi, 2008, 163–175 | MR

[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