REPRESENTATIONS OF ALGEBRAIC GROUPS OF TYPE D_n IN CHARACTERISTIC 2 WITH SMALL WEIGHT MULTIPLICITIES

摘要

Lower estimates for the maximal weight multiplicities in irreducible representations of algebraic groups of type D_n in characteristic 2 are found. If n ≥ 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.