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Representations of algebraic groups of type $$D_n$$ in characteristic 2 with small weight multiplicities. (English. Russian original) Zbl 1183.20050
J. Math. Sci., New York 161, No. 4, 558-564 (2009); translation from Zap. Nauchn. Semin. POMI 365, 182-195 (2009).
Summary: Lower estimates for the maximal weight multiplicities in irreducible representations of algebraic groups of type $$D_n$$ in characteristic 2 are found. lf $$n\geq 8$$, then either such a multiplicity is at least $$n-4-[n]_4$$, where $$[n]_4$$ is the residue of $$n$$ modulo 4, or all of its weight multiplicities are equal to 1. For groups of types $$B_n$$ and $$D_n$$ in odd characteristic and of type $$C_n$$, in characteristics greater than 7, similar results were obtained earlier.

##### MSC:
 20G05 Representation theory for linear algebraic groups 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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##### References:
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