Representations of algebraic groups of type C with small weight multiplicities.

Lower estimates for the maximal weight multiplicities in irreducible representations of the algebraic groups of type C in characteristic p ≤ 7 are found. If n ≥ 8 and p ≠ 2 , then for an irreducible representation either such a multiplicity is at least n− 4 − [ n],where [ n] is the residue of n modulo 4, or all the weight multiplicities are equal to 1.For p = 2, the situation is more complicated, and for every n and l there exists a class of representations with the maximal weight multiplicity equal to 2. For symplectic groups in characteristic p > 7 and spinor groups similar results were obtained earlier. Bibliography: 15 titles. [ABSTRACT FROM AUTHOR]