Representations of algebraic groups of type $D_n$ in characteristic 2 with small weight multiplicities

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.