UNIPOTENT ELEMENTS OF NONPRIME ORDER IN REPRESENTATIONS OF THE CLASSICAL ALGEBRAIC GROUPS: TWO BIG JORDAN BLOCKS

摘要

For irreducible rational representations of the classical algebraic groups in characteristic p ＞ 2, which are not equivalent to the composition of a group morphism and the standard representation, it is proved that usually the image of a unipotent element of order p~(s+1) ＞ p has at least two Jordan blocks of size ＞ p~s; all exceptions are indicated explicitly. As a corollary, irreducible rational representations of these groups whose images contain unipotent elements with just one Jordan block of size ＞ 1 are classified. Bibliography: 32 titles.