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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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