Modular representations of classical groups with small weight multiplicities.

Lower estimates for the maximal weight multiplicities in irreducible representations of the algebraic groups of types B n, C n, and D n in positive characteristic p are found under some minor restrictions on p. If G = B n( K), C n( K), or D n( K), n ≥ 8, p > 2 for types B n and D n and p > 7 for type C n, then either the maximal weight multiplicity for an irreducible representation of G is at least n − 7 or all its weight multiplicities are equal to 1. [ABSTRACT FROM AUTHOR]